Mathematica MathWorld Wolfram Science More »

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

The immersion of the Minkowski space in

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

(42 lines omitted)

Any minimal surface in Euclidean space

or any minimal time-like surface in Minkowski space

is generated by a holomorphic function

in the Gauss plane

; any maximal space-like surface in

is generated by a holomorphic function in the Lorentz plane

G. Ganchev, "Canonical Weierstrass Representation of Minimal Surfaces in Euclidean Space," arxiv.org/abs/0802.2374.

G. Ganchev, "Canonical Weierstrass Representation of Minimal and Maximal Surfaces in the Three-Dimensional Minkowski Space," arxiv.org/abs/0802.2632.

Report an issue »

	Source page:
	Email	Name (optional)
	Occupation (optional)	Organization (optional)
	I use Mathematica often occasionally never
	Country (optional) Remember me
	Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed. Privacy Policy »

RSS

Atom