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...
- 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...
- Thus, under this definition, a map is conformal if and only if it is biholomorphic. The two definitions for conformal maps are not equivalent. Being one-to-one...
- domain is a proper subdomain of C n {\displaystyle \mathbb {C} ^{n}} , biholomorphically equivalent to C n {\displaystyle \mathbb {C} ^{n}} . That is, an open...
- is not all of C {\displaystyle \mathbb {C} } , then there exists a biholomorphic mapping f {\displaystyle f} (i.e. a bijective holomorphic mapping whose...
- holomorphic maps is holomorphic. The two Riemann surfaces M and N are called biholomorphic (or conformally equivalent to emphasize the conformal point of view)...
- of G {\displaystyle G} as a neighbourhood of 0 {\displaystyle 0} ). Biholomorphic mapping – Bijective holomorphic function with a holomorphic inversePages...