### Abstract

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz–Minkowski 3-space R^{3}
_{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 R^{n+1}
_{1} that change type across an (n - 1)-dimensional light-like plane.

Original language | English |
---|---|

Pages (from-to) | 285-297 |

Number of pages | 13 |

Journal | Osaka Journal of Mathematics |

Volume | 52 |

Issue number | 1 |

Publication status | Published - 2015 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 52, no. 1, pp. 285-297.

}

TY - JOUR

T1 - Zero mean curvature surfaces in lorentz–minkowski 3-space which change type across a light-like line

AU - Fujimori, Shoichi

AU - Kim, Y. W.

AU - Koh, S. E.

AU - Rossman, W.

AU - Shin, H.

AU - Umehara, M.

AU - Yamada, K.

AU - Yang, S. D.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84925437757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925437757&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84925437757

VL - 52

SP - 285

EP - 297

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 1

ER -