-
biholomorphism or
biholomorphic function is a
bijective holomorphic function whose inverse is also holomorphic. Formally, a
biholomorphic function is a function...
-
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...
- 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...
- is not all of C {\displaystyle \mathbb {C} } , then
there exists a
biholomorphic mapping f {\displaystyle f} (i.e. a
bijective holomorphic mapping whose...
- 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...
-
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...
-
holomorphic maps is holomorphic. The two
Riemann surfaces M and N are
called biholomorphic (or
conformally equivalent to
emphasize the
conformal point of view)...
-
considered as a
Riemann surface, the open unit disk is
isomorphic ("
biholomorphic", or "conformally equivalent") to the
upper half-plane, and the two...
