Trivalent Maximal Surfaces in Minkowski Space

Wai Yeung Lam, Masashi Yasumoto

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We investigate discretizations of maximal surfaces in Minkowski space, which are surfaces with vanishing mean curvature. The corresponding discrete surfaces admit a Weierstrass-type representation in terms of discrete holomorphic quadratic differentials. There are two particular types of discrete maximal surfaces that are obtained by taking the real part and the imaginary part of the representation formula, and they are deformable to each other by a one-parameter family. We further introduce a compatible notion of vertex normals for general trivalent surfaces to characterize their singularities in Minkowski space as in the smooth theory.

Original languageEnglish
Title of host publicationLorentzian Geometry and Related Topics - GeLoMa 2016
EditorsMaría A. Canadas-Pinedo, Francisco J. Palomo, Jose Luis Flores
PublisherSpringer New York LLC
Pages169-184
Number of pages16
ISBN (Print)9783319662893
DOIs
Publication statusPublished - 2017
Externally publishedYes
Event8th International Meeting on Lorentzian Geometry,GeLoMa 2016 - Malaga, Spain
Duration: Sep 20 2016Sep 23 2016

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume211
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference8th International Meeting on Lorentzian Geometry,GeLoMa 2016
CountrySpain
CityMalaga
Period9/20/169/23/16

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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