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Bijective holomorphic function with a holomorphic inverse
or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose
Biholomorphism
Type of mathematical functions
holomorphic. At this time, ϕ {\displaystyle \phi } is called a U, V biholomorphism also, we say that U and V are biholomorphically equivalent or that they
Function of several complex variables
Function_of_several_complex_variables
Type of mathematical space
compact Hermitian symmetric spaces: K is the isometry group, and G is the biholomorphism group of M. Over the real numbers, a real flag manifold is also called
Generalized_flag_variety
Study of complex manifolds and several complex variables
(U_{1}\cap U_{2})\to \psi (U_{1}\cap U_{2})} is a biholomorphism. Notice that since every biholomorphism is a diffeomorphism, and C n {\displaystyle \mathbb
Complex_geometry
{\displaystyle [1:x_{1}:\dots :x_{n}]} of the projective space thus defines a biholomorphism. This model is the equivalent of the Poincaré disk model. Unlike the
Complex_hyperbolic_space
Manifold with inversion symmetry
bounded symmetric domain if for every x in Ω, there is an involutive biholomorphism σx of Ω for which x is an isolated fixed point. The Harish-Chandra embedding
Hermitian_symmetric_space
Manifold upon which it is possible to perform calculus
collection of all local Ck diffeomorphisms on Rn form a pseudogroup. All biholomorphisms between open sets in Cn form a pseudogroup. More examples include:
Differentiable_manifold
Mathematical theorem, used in calculus
\mathbb {C} } , and assume that f : U → V {\displaystyle f:U\to V} is a biholomorphism. Then f {\displaystyle f} and f − 1 {\displaystyle f^{-1}} have antiderivatives
Integral_of_inverse_functions
examples determined up to isometry, or 100 fake projective planes up to biholomorphism. A surface of general type with the same Betti numbers as a minimal
Fake_projective_plane
Nonlinear differential operator used to study conformal mappings
a biholomorphisms is locally in Γ, then it too is in Γ. The pseudogroup is said to be transitive if, given z and w in C, there is a biholomorphism f in
Schwarzian_derivative
{\displaystyle L^{2}} inner product on this space is manifestly invariant under biholomorphisms of D, the Bergman kernel and the associated Bergman metric are therefore
Bergman_kernel
mappings of G to another domain G ′ {\displaystyle G'} . That is if f is a biholomorphism of G and G ′ {\displaystyle G'} , then d G ( p , q ) = d G ′ ( f ( p
Bergman_metric
Concept in mathematics
anti-biholomorphic if they are homotopic to each other; the biholomorphism (or anti-biholomorphism) is precisely the harmonic map produced as the limit of
Harmonic_map
Graph drawing used to study Riemann surfaces
{\displaystyle f} is sufficient to describe f {\displaystyle f} itself up to biholomorphism. However, this construction identifies the Riemann surface only as a
Dessin_d'enfant
biholomorphism f : Ω → C n {\displaystyle f:\Omega \rightarrow \mathbb {C} ^{n}} , f − 1 {\displaystyle f^{-1}} is not a polynomial. Biholomorphism preserves
Fatou–Bieberbach_domain
structures of X0 and Xb because they are induced by diffeomorphisms, not biholomorphisms. Let FpHk(Xb, C) denote the pth step of the Hodge filtration. The Hodge
Period_mapping
G=\operatorname {Aut} (D)^{\circ }} be the identity component of its biholomorphism group. Then the Shilov boundary S {\displaystyle S} is the smallest
Shilov_boundary
Vector bundles theorem
smooth structure E → ( X , ω ) {\displaystyle E\to (X,\omega )} up to biholomorphism, and the moduli space of Hermite–Einstein metrics on the complex vector
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
disc of f around the point z 0 {\displaystyle z_{0}} if there exists a biholomorphism ϕ : U → D {\displaystyle \phi :U\to \mathbb {D} } where D {\displaystyle
Siegel_disc
Mathematical concept
Andrew (2019). "Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents". Mathematische Annalen. 374 (3–4): 1811–1844
Pseudoconvexity
Correspondsnce between Higgs bundles and fundamental group representations
T^{*}\operatorname {Jac} (X)\cong (\mathbb {C} ^{*})^{2g}} which is not a biholomorphism. One can check that the natural complex structures on these two spaces
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
Open convex self-dual cones
HT be the group of biholomorphisms of the tube T. The Cayley transform shows that is isomorphic to the group HD of biholomorphisms of the bounded domain
Symmetric_cone
Polish mathematician and political activist (1947–2022)
R. Bell on the Feferman–Vaught theorem on the smooth extension of biholomorphisms to the boundaries of their domains. This work, which was published
Ewa_Ligocka
Polygon associated with a compact Riemann surface
transformations of X and can be identified with a subgroup Γ of the group of biholomorphisms of X. The group Γ thus acts freely on X with compact quotient space
Fundamental_polygon
compact. Loos (1977) uses the Bergman operators to construct an explicit biholomorphism between X and a closed smooth algebraic subvariety of complex projective
Mutation_(Jordan_algebra)
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