Semi-discrete Maximal Surfaces with Singularities in Minkowski Space

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

Abstract

We investigate semi-discrete maximal surfaces with singularities in Minkowski 3-space. In the smooth case, maximal surfaces (spacelike surfaces with mean curvature identically 0) in Minkowski 3-space admit a Weierstrass-type representation and they generally have singularities. In this paper, we first describe semi-discrete isothermic maximal surfaces in Minkowski 3-space and give a Weierstrass-type representation for them determined from integrable system principles. Furthermore, we show that semi-discrete isothermic maximal surfaces admit associated one-parameter families of deformations whose mean curvature remains identically 0. Finally we give a criterion that naturally describes the unified scheme of the “singular set” for these semi-discrete maximal surfaces, including the associated family.

Original languageEnglish
Title of host publicationMinimal Surfaces
Subtitle of host publicationIntegrable Systems and Visualisation - Workshops, 2016-19
EditorsTim Hoffmann, Martin Kilian, Katrin Leschke, Francisco Martin
PublisherSpringer
Pages263-280
Number of pages18
ISBN (Print)9783030685409
DOIs
Publication statusPublished - 2021
Externally publishedYes
EventWorkshop Series of Minimal Surfaces: Integrable Systems and Visualisation, 2016-19 - Cork, Ireland
Duration: Mar 27 2017Mar 29 2017

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume349
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceWorkshop Series of Minimal Surfaces: Integrable Systems and Visualisation, 2016-19
Country/TerritoryIreland
CityCork
Period3/27/173/29/17

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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