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Mathematical concept
analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective. The function f : z ↦ 2 z + z 2 {\displaystyle
Univalent_function
Statement in complex analysis; formerly the Bieberbach conjecture
coefficients a n {\displaystyle a_{n}} of a univalent function, i.e., a one-to-one holomorphic function that maps the unit disk into the complex plane
De_Branges's_theorem
Statement in complex analysis
absolute value 1 {\displaystyle 1} . The Koebe function and its rotations are schlicht: that is, univalent (analytic and one-to-one) and satisfying f (
Koebe_quarter_theorem
Study of space and shapes locally given by a convergent power series
analogues and generalizations". A holomorphic function on an open subset of the complex plane is called univalent if it is injective. One can prove that if
Geometric_function_theory
Topics referred to by the same term
Univalent may refer to: Univalent function – an injective holomorphic function on an open subset of the complex plane Univalent foundations – a type-based
Univalent
family of holomorphic functions on the disk with positive real part. The Loewner semigroup generalizes the notion of a univalent semigroup. The Loewner
Loewner_differential_equation
Mathematical theorem
of univalent holomorphic functions on an open domain has a uniform limit on compacta, then either the limit is constant or the limit is univalent. If
Riemann_mapping_theorem
Gabriel Koenigs, it gives a canonical representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the
Koenigs_function
Characterization of starlike univalent holomorphic functions
holomorphic univalent functions on the unit disk which are starlike. Nevanlinna used this criterion to prove the Bieberbach conjecture for starlike univalent functions
Nevanlinna's_criterion
Function that preserves distinctness
mathematical functions Injective metric space – Type of metric space Monotonic function – Order-preserving mathematical function Univalent function – Mathematical
Injective_function
Matrix used in complex analysis
the univalent function itself. The Grunsky matrix and its associated inequalities were originally formulated in a more general setting of univalent functions
Grunsky_matrix
95–115, doi:10.1007/bf01449883, S2CID 116695038 Duren, P. L. (1983), Univalent functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer-Verlag
Positive_harmonic_function
concerning holomorphic univalent functions defined on the unit disk in the complex numbers. The theorem states that a univalent function defined on the unit
Grunsky's_theorem
Association of one output to each input
Sarikaya, Deniz (eds.). Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Synthese Library. Vol. 407
Function_(mathematics)
Type theory in logic and mathematics
between the work referred to as homotopy type theory, and that called the univalent foundations project. Although neither is precisely delineated, and the
Homotopy_type_theory
Mathematics award
"Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions of several complex variables, and in
Fields_Medal
for functions of the form P ∘ ϕ {\displaystyle P\circ \phi } where P {\displaystyle P} is a polynomial and ϕ {\displaystyle \phi } is univalent. Goodman
Goodman's_conjecture
Mathematical concept
Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types. Types
Univalent_foundations
Languages. The MIT Press. function type at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program, Institute
Function_type
uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0, can
Carathéodory_kernel_theorem
American mathematician
graph theory and to the theory of univalent functions: The conjecture on the coefficients of multivalent functions named after him is considered the most
Adolph_Winkler_Goodman
states that there is a nonconstant single-valued holomorphic function (univalent function) on such a Riemann surface. It is a generalization of the Runge
Behnke–Stein theorem on Stein manifolds
Behnke–Stein_theorem_on_Stein_manifolds
Complex analysis function
Publications. ISBN 0-486-67748-6. Marvin Rosenblum and James Rovnyak (1994). Topics in Hardy Classes and Univalent Functions. Springer. ISBN 3-7643-5111-X.
Nevanlinna_function
Function whose actual domain of definition may be smaller than its apparent domain
element of the second set; it is thus a univalent relation. This generalizes the concept of a (total) function by not requiring every element of the first
Partial_function
Limit of roots of sequence of functions
univalent functions on a connected open set G that converge uniformly on compact subsets of G to a holomorphic function f, then either f is univalent
Hurwitz's theorem (complex analysis)
Hurwitz's_theorem_(complex_analysis)
Type of differential equation
{w''}{w'}}\right)^{2}=f} which occurs in the theory of conformal mapping and univalent functions. In this case the ODEs are in the complex domain and differentiation
Riccati_equation
Class of mathematical functions
classes and univalent functions. Birkhauser Advanced Texts: Basel Textbooks. Basel: Birkhauser Verlag. Conway, John B. (1978). Functions of one complex
Subharmonic_function
Nonlinear differential operator used to study conformal mappings
theory of modular forms and hypergeometric functions. It plays an important role in the theory of univalent functions, conformal mapping and Teichmüller spaces
Schwarzian_derivative
Topics referred to by the same term
local uniform convergence of univalent functions Borel–Carathéodory theorem, about the boundedness of a complex analytic function Vitali–Carathéodory theorem
Carathéodory's_theorem
Mathematician specializing in complex analysis and differential equations
1915 – 1978) was a mathematician who worked on Complex Analysis, Univalent Functions Theory, and Differential and Integral Equations. He was a student
Zeev_Nehari
Mathematical theorem in real analysis
Titchmarsh's The Theory of Functions. Titchmarsh uses the terms 'simple' and 'schlicht' (function) in place of 'univalent'. Univalent means holomorphic and
Uniform_limit_theorem
Theorem in complex analysis
Carathéodory's results on prime ends and the boundary behaviour of univalent holomorphic functions. The first proof of Carathéodory's theorem presented here is
Carathéodory's theorem (conformal mapping)
Carathéodory's_theorem_(conformal_mapping)
Landau's constants Holomorphic functions are analytic Schwarzian derivative Analytic capacity Disk algebra Univalent function Ahlfors theory Bieberbach conjecture
List of complex analysis topics
List_of_complex_analysis_topics
American mathematician (1935–2020)
{\displaystyle H^{p}} -Spaces, Academic Press, Dover 2000 1983: Univalent Functions, Grundlehren der mathematischen Wissenschaften, Springer Verlag 1988:
Peter_Duren
British mathematician (1926–2020)
Zbl 0851.42009. Hayman, W. K. (2002), "Univalent and Multivalent Functions", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex Analysis
Walter_Hayman
Unsolved mathematical problem
June 2007). "Smale's mean value conjecture and the coefficients of univalent functions" (PDF). Proceedings of the American Mathematical Society. 135 (10):
Mean_value_problem
Theorem in topology
Mathematical Society, ISBN 0-8218-1040-5 Pommerenke, C. (1975), Univalent functions, with a chapter on quadratic differentials by Gerd Jensen, Studia
Janiszewski's_theorem
Romanian mathematician (1931–2016)
Gheorghe Călugăreanu, was titled Variational methods in the theory of univalent functions. He continued as faculty at Babeș-Bolyai University, rising to the
Petru_Mocanu
American mathematician (1939–2003)
including Fourier analysis, summability methods, univalent function, orthogonal polynomials and special functions. He made contributions to all of these topics
Joaquín_Bustoz_Jr.
American mathematician
and numerical analysis; he has also worked in hyperbolic geometry, univalent function theory, several complex variables, microlocal analysis and index theory
Charles Epstein (mathematician)
Charles_Epstein_(mathematician)
coefficients of univalent functions, Doklady of Soviet Academy of Sciences, 1965, v. 160, 4, 769 - 771. Milin I.M. On coefficients of univalent functions, Doklady
Isaak_Moiseevich_Milin
Topics referred to by the same term
computer programming, a feature, type, or function related to a monad (functional programming) Monadic or univalent, a chemical valence Monadic, in theology
Monadic
Typographic symbol
Wolfram MathWorld. Retrieved 2020-08-24. Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics (GitHub version)
Vertical_bar
Concept in probability theory
to Schramm–Loewner evolutions (PDF) Pommerenke, Christian (1975), Univalent functions, with a chapter on quadratic differentials by Gerd Jensen, Studia
Schramm–Loewner_evolution
Quasiconformal complex image of a circle
that this result can be applied to uniformly bounded holomorphic univalent functions f(z) on the unit disk D. Let Ω = f(D). As Carathéodory had proved
Quasicircle
American mathematician
1090/S0002-9947-1974-0344468-7. Baernstein, Albert (1974). "Integral means, univalent functions and circular symmetrization". Acta Mathematica. 133 (1): 139–169
Albert_Baernstein_II
Series of mathematics textbooks
Holomorphic Functions and Integral Representations in Several Complex Variables, R. Michael Range (1986, ISBN 978-0-387-96259-7) Univalent Functions and Teichmüller
Graduate_Texts_in_Mathematics
Topics referred to by the same term
Weissbach; 1915–1978), mathematician who worked on Complex Analysis, Univalent Functions Theory and Differential and Integral Equations Weißbach, Baden-Württemberg
Weissbach
Irish mathematician and chess player
With J. B. Twomey, "Some properties of bounded univalent functions and related classes of functions". "Fourier series with gaps". "Fourier series with
Patrick_Brendan_Kennedy
Reasoning about equations with free variables
identity on the domain of R. But a univalent relation is only a partial function, while a univalent total relation is a function. The formula for totality is
Algebraic_logic
Mathematics theorem
holomorphic univalent self-mapping of the unit disk in the complex numbers that fixes 0 induces a contractive composition operator on various function spaces
Littlewood subordination theorem
Littlewood_subordination_theorem
German mathematician (1933–2024)
of 1992 original){{cite book}}: CS1 maint: postscript (link) Univalent Functions. Vandenhoeck & Ruprecht. 1975. ISBN 978-3525401330. With Gerd Jensen
Christian_Pommerenke
Logic principle
equality Type theory Univalence axiom The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton, NJ:
Extensionality
Mathematical-logic system
Languages, p. 273, Benjamin C. Pierce "Scott's Representation Theorem and the Univalent Karoubi Envelope" (PDF). Dagstuhl Publishing. Retrieved 2026-05-19. Pierce
Lambda_calculus
Finnish mathematician (1925–2020)
2nd edition: Quasiconformal mappings in the plane. Springer 1973. Univalent functions and Teichmüller Spaces. Springer, Graduate Texts in Mathematics,
Olli_Lehto
German mathematician (1902–1993)
mathematician known primarily for his work on complex analysis, specifically univalent functions and conformal mappings, and graph theory. He was the first to introduce
Herbert_Grötzsch
Romanian mathematician
1963. Călugăreanu studied the theory of functions of a complex variable (meromorphic functions, univalent functions, analytic extension invariants), as well
Gheorghe_Călugăreanu
Mathematics, vol. 183, Birkhäuser, ISBN 0-8176-3904-7 Lehto, Olli (1987), Univalent functions and Teichmüller spaces, Graduate Texts in Mathematics, vol. 109,
Busemann_function
Extends the Jordan curve theorem to characterize the inner and outer regions
(2nd ed.), Springer, ISBN 9781461411048 Pommerenke, Christian (1975), Univalent functions, with a chapter on quadratic differentials by Gerd Jensen, Studia
Schoenflies_problem
Swiss mathematician (1923–1987)
Fourier analysis—Cauchy integrals—construction of conformal maps—univalent functions. Wiley. ISBN 0-471-08703-3. Golub, Gene H.; Varga, Richard S. (1988)
Peter_Henrici_(mathematician)
Canadian–American mathematician
1090/S0002-9939-1953-0058716-6. Jenkins, James A. (1953). "Various remarks on univalent functions". Proceedings of the American Mathematical Society. 4 (4): 595. doi:10
James_Allister_Jenkins
Type of mathematical functions
analogues of affine varieties or affine schemes in algebraic geometry. If the univalent domain on C n {\displaystyle \mathbb {C} ^{n}} is connection to a manifold
Function of several complex variables
Function_of_several_complex_variables
in Lawler, Schramm & Werner (2002). Pommerenke, Christian (1975). Univalent functions. Studia Mathematica/Mathematische Lehrbücher. Vol. Band XXV. With
Conformal_radius
Statement in complex analysis
Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by Fekete and Szegő (1933), related to the Bieberbach conjecture
Fekete–Szegő_inequality
American mathematician
Journal of Mathematics and Mathematical ..., 1983, hindawi.com "Univalent functions with univalent derivatives", SM Shah, SY Trimble, Bulletin of the American
S._M._Shah
Chemical compound
February 1971). "Stability constants of cyclic polyether complexes with univalent cations". Journal of the American Chemical Society. 93 (3): 600–606. doi:10
21-Crown-7
Reversal of the order of elements of a binary relation
total then it is a function. When QT is univalent, then Q is termed injective. When QT is total, Q is termed surjective. If Q is univalent, then QQT is an
Converse_relation
American mathematician
thesis was entitled A Boundary Value Problem Arising in the Theory of Univalent Functions and was supervised by Paul Garabedian. He then took a position as
Jerry_Kazdan
Inequality on the coefficients of the exponential of a power series
Coefficient Bounds in the Theory of Univalent Functions and Nonoverlapping Domains", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex Analysis
Lebedev–Milin_inequality
Coefficient Bounds in the Theory of Univalent Functions and Nonoverlapping Domains", in Kuhnau, Reiner (ed.), Geometric Function Theory, Handbook of Complex Analysis
Nikolai_Andreevich_Lebedev
Type of musical chord
Heinrich Schenker. He explained that although there is a kinship between all univalent chords rising out of the fifth degree, the dominant ninth chord is not
Diminished_seventh_chord
computational interpretation to univalent foundations (also known as homotopy type theory). In cubical type theory, function extensionality and univalence
Cubical_type_theory
Partial differential equation
Wissenschaften, vol. 126 (2nd ed.), Springer-Verlag Lehto, Olli (1987), Univalent functions and Teichmüller spaces, Graduate Texts in Mathematics, vol. 109,
Beltrami_equation
American mathematician
--On certain coefficients of univalent functions, by J.A. Jenkins. Selected Topics in the Classical Theory of Functions of a Complex Variable, Holt, Rinehart
Maurice_Heins
Rosenblum, Marvin; Rovnyak, James (1994). Topics in Hardy classes and univalent functions. Birkhauser Advanced Texts: Basel Textbooks. Basel: Birkhauser Verlag
Bounded_type_(mathematics)
Mathematical constructs and creation rules
deprecated parameter |citeseerx= (help) Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for
Inductive_type
Process in geometric function theory
their boundary circles. This problem can be reduced to that of finding univalent holomorphic maps f, g of the unit disk and its complement into the extended
Conformal_welding
Generalization of the real numbers
(paperback), ISBN 0-7456-3878-3 (hardcover). The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton, NJ:
Surreal_number
Polygon associated with a compact Riemann surface
Probability Theory, Springer, ISBN 978-3-7643-6441-0 Lehto, Olli (1987), Univalent functions and Teichmüller spaces, Graduate Texts in Mathematics, vol. 109,
Fundamental_polygon
Branch of mathematics that studies sets
nLab Homotopy Type Theory: Univalent Foundations of Mathematics Archived 2021-01-22 at the Wayback Machine. The Univalent Foundations Program. Institute
Set_theory
Mathematical concept
univalent holomorphic map of the unit disk D onto Ω extending to a smooth diffeomorphism of the circle onto ∂Ω. If χΩ is the characteristic function of
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
Addition, multiplication, division, ...
domain is that a relation that corresponds to a binary operation is a univalent relation. Hyperoperation Infix notation Operator (mathematics) Order of
Operation_(mathematics)
German-born American mathematician
Michael Fekete. In his dissertation on Conformal representation and univalent functions he introduced the "Schiffer variation", a method for handling geometric
Menahem_Max_Schiffer
German mathematician (1882–1945)
Mathematics Archive, University of St Andrews Duren, Peter L. (1983), Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles
Paul_Koebe
Washington University in St. Louis Geometric studies in the theory of univalent functions Louis Nirenberg New York University Also won 1975 Gerald Enoch Sacks
List of Guggenheim Fellowships awarded in 1966
List_of_Guggenheim_Fellowships_awarded_in_1966
17. ISBN 9783939897873. S2CID 15020752. Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for
Polynomial functor (type theory)
Polynomial_functor_(type_theory)
Binary relation over a set and itself
reflexivity. A univalent relation may also be called a partial function. A (total) function is a partial function that is left-total. An injective function (or partial
Homogeneous_relation
Result of multiplying types in type theory
type product type at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program, Institute for Advanced Study
Product_type
Combining capacity of elements with other atoms
the compound. Valence is defined by the IUPAC as: The maximum number of univalent atoms (originally hydrogen or chlorine atoms) that may combine with an
Valence_(chemistry)
Mathematical theory of data types
doi:10.1007/BF00484985. ISSN 1573-0964. The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Homotopy Type
Type_theory
Theorem in homotopy theory
and Whitehead's principle.". Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Foundations Program Institute for Advanced Study
Whitehead_theorem
Relationship between elements of two sets
1} to 0 {\displaystyle 0} ). Functional (also called right-unique or univalent): for all x ∈ X {\displaystyle x\in X} and all y , z ∈ Y , {\displaystyle
Binary_relation
of functions, harmonic analysis, theory of analytic functions and a fundamental contribution to the classical theory of univalent analytic functions. He
Mkhitar_Djrbashian
chromosome pairs (bivalents) or single chromosomes without mating partners (univalents), or even whole sets of chromosomes, in that these are separated according
Non-random segregation of chromosomes
Non-random_segregation_of_chromosomes
become applicable to multiple different models. For example, reasoning in univalent foundations yields theorems about arbitrary (∞, 1)-toposes. Furthermore
Synthetic_mathematics
Relationship between programs and proofs
AI]. Baez & Stay 2011. Homotopy Type Theory: Univalent Foundations of Mathematics. (2013) The Univalent Foundations Program. Institute for Advanced Study
Curry–Howard_correspondence
Chemical group (–SO2–C6H4–CH3)
chemistry, a toluenesulfonyl group (tosyl group, abbreviated Ts or Tos) is a univalent functional group with the chemical formula −SO2−C6H4−CH3. It consists
Tosyl_group
Statement in complex analysis
injective; that is, univalent. The Koebe 1/4 theorem provides a related estimate in the case that f {\displaystyle f} is univalent. Nevanlinna–Pick interpolation
Schwarz_lemma
Toxic effects of thallium
thallium's high toxicity is that when present in aqueous solution as the univalent thallium(I) ion (Tl+) it exhibits some similarities with essential alkali
Thallium_poisoning
Pudlák 2013, page 13 Pudlák 2013, page 22 The Univalent Foundations Program 2013, Subsection "Univalent foundations" of Introduction Pudlák 2013, page
Equivalent definitions of mathematical structures
Equivalent_definitions_of_mathematical_structures
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