mathlib3 documentation

analysis.complex.conformal

Conformal maps between complex vector spaces #

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We prove the sufficient and necessary conditions for a real-linear map between complex vector spaces to be conformal.

Main results #

Warning #

Antiholomorphic functions such as the complex conjugate are considered as conformal functions in this file.

A real continuous linear map on the complex plane is conformal if and only if the map or its conjugate is complex linear, and the map is nonvanishing.