論文

査読有り
2016年12月

ENTIRE ZERO-MEAN CURVATURE GRAPHS OF MIXED TYPE IN LORENTZ-MINKOWSKI 3-SPACE

QUARTERLY JOURNAL OF MATHEMATICS
  • Shoichi Fujimori
  • ,
  • Yu Kawakami
  • ,
  • Masatoshi Kokubu
  • ,
  • Wayne Rossman
  • ,
  • Masaaki Umehara
  • ,
  • Kotaro Yamada

67
4
開始ページ
801
終了ページ
837
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1093/qmath/haw038
出版者・発行元
OXFORD UNIV PRESS

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-1(3) is called of mixed type if it changes causal type from space-like to time-like. In R-1(3), 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.

Web of Science ® 被引用回数 : 9

リンク情報
DOI
https://doi.org/10.1093/qmath/haw038
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000393319000015&DestApp=WOS_CPL