WOLFRAM|DEMONSTRATIONS PROJECT

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

space

Euclidean

Minkowski time-like

Minkowski space-like

part

real

imaginary

opacity

1

The holomorphic function

w=log(z)

in the Gauss plane generates a minimal surface in Euclidean space

3



and a minimal time-like surface in Minkowski space

3



1

; the same holomorphic function in the Lorentz plane generates a maximal space-like surface in

3



1

.

The immersion of the Minkowski space in

3



is used to present the minimal time-like surface and the maximal space-like surface in

3



1

.