Singularities of maximal surfaces

Shoichi Fujimori; Kentaro Saji; Masaaki Umehara; Kotaro Yamada

doi:10.1007/s00209-007-0250-0

Singularities of maximal surfaces

Shoichi Fujimori, Kentaro Saji, Masaaki Umehara, Kotaro Yamada

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

72 Citations (Scopus)

Abstract

We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.

Original language	English
Pages (from-to)	827-848
Number of pages	22
Journal	Mathematische Zeitschrift
Volume	259
Issue number	4
DOIs	https://doi.org/10.1007/s00209-007-0250-0
Publication status	Published - Aug 2008

Keywords

Cuspidal cross cap
De Sitter space
Maximal surfaces
Minkowski space

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-007-0250-0

Cite this

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title = "Singularities of maximal surfaces",

abstract = "We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.",

keywords = "Cuspidal cross cap, De Sitter space, Maximal surfaces, Minkowski space",

author = "Shoichi Fujimori and Kentaro Saji and Masaaki Umehara and Kotaro Yamada",

note = "Funding Information: Kentaro Saji was supported by JSPS Research Fellowships for Young Scientists. Masaaki Umehara and Kotaro Yamada were supported by Grant-in-Aid for Scientific Research (No. 15340024(B)) and (No. 14340024(B)), respectively. ",

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AU - Fujimori, Shoichi

AU - Saji, Kentaro

AU - Umehara, Masaaki

AU - Yamada, Kotaro

N1 - Funding Information: Kentaro Saji was supported by JSPS Research Fellowships for Young Scientists. Masaaki Umehara and Kotaro Yamada were supported by Grant-in-Aid for Scientific Research (No. 15340024(B)) and (No. 14340024(B)), respectively.

PY - 2008/8

Y1 - 2008/8

N2 - We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.

AB - We show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.

KW - Cuspidal cross cap

KW - De Sitter space

KW - Maximal surfaces

KW - Minkowski space

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JF - Mathematische Zeitschrift

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ER -

Singularities of maximal surfaces

Abstract

Keywords

ASJC Scopus subject areas

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