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

Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada

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7 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)801-837
Number of pages37
JournalQuarterly Journal of Mathematics
Volume67
Issue number4
DOIs
Publication statusPublished - Dec 1 2016

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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fujimori, S., Kawakami, Y., Kokubu, M., Rossman, W., Umehara, M., & Yamada, K. (2016). Entire zero-mean curvature graphs of mixed type in lorentz-minkowski 3-space. Quarterly Journal of Mathematics, 67(4), 801-837. https://doi.org/10.1093/qmath/haw038