Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line

Shoichi Fujimori, Y. W. Kim, S. E. Koh, W. Rossman, H. Shin, M. Umehara, K. Yamada, S. D. Yang

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz–Minkowski 3-space R3 1 have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across a light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in Rn+1 1 that change type across an (n - 1)-dimensional light-like plane.

Original languageEnglish
Pages (from-to)285-297
Number of pages13
JournalOsaka Journal of Mathematics
Volume52
Issue number1
Publication statusPublished - 2015

Fingerprint

Mean Curvature
Maximal Surfaces
Spacelike Surface
Singular Set
Line
Zero
Minimal surface
Continuation
Hypersurface
Corollary
Singularity
Family

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fujimori, S., Kim, Y. W., Koh, S. E., Rossman, W., Shin, H., Umehara, M., ... Yang, S. D. (2015). Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line. Osaka Journal of Mathematics, 52(1), 285-297.

Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line. / Fujimori, Shoichi; Kim, Y. W.; Koh, S. E.; Rossman, W.; Shin, H.; Umehara, M.; Yamada, K.; Yang, S. D.

In: Osaka Journal of Mathematics, Vol. 52, No. 1, 2015, p. 285-297.

Research output: Contribution to journalArticle

Fujimori, S, Kim, YW, Koh, SE, Rossman, W, Shin, H, Umehara, M, Yamada, K & Yang, SD 2015, 'Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line', Osaka Journal of Mathematics, vol. 52, no. 1, pp. 285-297.
Fujimori S, Kim YW, Koh SE, Rossman W, Shin H, Umehara M et al. Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line. Osaka Journal of Mathematics. 2015;52(1):285-297.
Fujimori, Shoichi ; Kim, Y. W. ; Koh, S. E. ; Rossman, W. ; Shin, H. ; Umehara, M. ; Yamada, K. ; Yang, S. D. / Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line. In: Osaka Journal of Mathematics. 2015 ; Vol. 52, No. 1. pp. 285-297.
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