# Minimal and Maximal Surfaces Generated by the Holomorphic Function log(z)

Minimal and Maximal Surfaces Generated by the Holomorphic Function log(z)

The holomorphic function in the Gauss plane generates a minimal surface in Euclidean space and a minimal time-like surface in Minkowski space ; the same holomorphic function in the Lorentz plane generates a maximal space-like surface in .

w=log(z)

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The immersion of the Minkowski space in is used to present the minimal time-like surface and the maximal space-like surface in .

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