### Abstract

It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R^{3}
_{1}is called of mixed type if it changes causal type from space-like to time-like. In R^{3}
_{1} Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.

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

Pages (from-to) | 801-837 |

Number of pages | 37 |

Journal | Quarterly Journal of Mathematics |

Volume | 67 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Quarterly Journal of Mathematics*,

*67*(4), 801-837. https://doi.org/10.1093/qmath/haw038

**Entire zero-mean curvature graphs of mixed type in lorentz-minkowski 3-space.** / Fujimori, Shoichi; Kawakami, Yu; Kokubu, Masatoshi; Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro.

Research output: Contribution to journal › Article

*Quarterly Journal of Mathematics*, vol. 67, no. 4, pp. 801-837. https://doi.org/10.1093/qmath/haw038

}

TY - JOUR

T1 - Entire zero-mean curvature graphs of mixed type in lorentz-minkowski 3-space

AU - Fujimori, Shoichi

AU - Kawakami, Yu

AU - Kokubu, Masatoshi

AU - Rossman, Wayne

AU - Umehara, Masaaki

AU - Yamada, Kotaro

PY - 2016/12/1

Y1 - 2016/12/1

N2 - It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R3 1is called of mixed type if it changes causal type from space-like to time-like. In R3 1 Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.

AB - It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R3 1is called of mixed type if it changes causal type from space-like to time-like. In R3 1 Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.

UR - http://www.scopus.com/inward/record.url?scp=85041631699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041631699&partnerID=8YFLogxK

U2 - 10.1093/qmath/haw038

DO - 10.1093/qmath/haw038

M3 - Article

VL - 67

SP - 801

EP - 837

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 4

ER -