Bijective holomorphic function with a holomorphic inverse
The complex exponential function mapping biholomorphically a rectangle to a quarter-annulus.
In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic.
or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose...
(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...
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...
\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...
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...
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...
[1:x_{1}:\dots :x_{n}]} of the projective space thus defines the required biholomorphism. This model is the equivalent of the Poincaré disk model. Unlike the...
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...
collection of all local Ck diffeomorphisms on Rn form a pseudogroup. All biholomorphisms between open sets in Cn form a pseudogroup. More examples include:...
anti-biholomorphic if they are homotopic to each other; the biholomorphism (or anti-biholomorphism) is precisely the harmonic map produced as the limit of...
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...
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...
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...
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...
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...
{\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...
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...
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...
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