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biholomorphic function

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Definition

A biholomorphic function is a holomorphic function which is a bijection on the underlying sets and whose set-theoretic inverse is also holomorphic.

Properties

If f:Uβ†’Vf:U\to V is a bijective holomorphic map of open subsets of complexfied Cartesian space β„‚ n{\mathbb{C}}^n, then the determinant of the Jacobian J(f)J(f) is nowhere 00, that is f βˆ’1f^{-1} is holomorphic.

(See this MO discussion and also this other MO discussion)

References

  • Eric Bedford, What is… a Biholomorphic Mapping, Notices of the AMS,volume 59, number 6 (pdf)

Last revised on July 19, 2014 at 20:49:23. See the history of this page for a list of all contributions to it.