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

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .

[more]

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

[less]

Contributed by: Georgi Ganchev and Radostina Encheva (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send