### 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 |
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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.