Definition of Biholomorphically. Meaning of Biholomorphically. Synonyms of Biholomorphically

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Definition of Biholomorphically

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Meaning of Biholomorphically from wikipedia

- \phi \colon U\to V} , we say that U and V are biholomorphically equivalent or that they are biholomorphic. If n = 1 , {\displaystyle n=1,} every simply...
- n>1} , open balls and open polydiscs are not biholomorphically equivalent, that is, there is no biholomorphic mapping between the two. This was proven by...
- between charts are biholomorphic, complex manifolds are, in particular, smooth and canonically oriented (not just orientable: a biholomorphic map to (a subset...
- around every point on the sphere there is a neighborhood that can be biholomorphically identified with C {\displaystyle \mathbf {C} } . On the other hand...
- of G {\displaystyle G} as a neighbourhood of 0 {\displaystyle 0} ). Biholomorphic mapping – Bijective holomorphic function with a holomorphic inversePages...
- considered as a Riemann surface, the open unit disk is isomorphic ("biholomorphic", or "conformally equivalent") to the upper half-plane, and the two...
- theorem says that a simply connected domain in the complex plane is "biholomorphically equivalent" (i.e. there is a bijection between them that is holomorphic...
- curvature. Then the universal cover of M, with its natural metric, is biholomorphically isometric to the metric product of complex Euclidean space, with some...
- isometry group. In the category of Riemann surfaces, an automorphism is a biholomorphic map (also called a conformal map), from a surface to itself. For example...
- a Riemann surface, every point admits an open neighborhood which is biholomorphic to an open subset of the complex plane. Thereby the notion of a meromorphic...