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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Bernstein type theorems in Finsler spaces with the volume form induced from the projective sphere bundle
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by Qun He and Yi-Bing Shen PDF
Proc. Amer. Math. Soc. 134 (2006), 871-880 Request permission

Abstract:

By using the volume form induced from the projective sphere bundle of the Finsler manifold, we study the Finsler minimal submanifolds. It is proved that such a volume form for the Randers metric $F=\alpha +\beta$ in a Randers space is just that for the Riemannian metric $\alpha$, and therefore the Bernstein type theorem in the special Randers space of dimension $\leq 8$ is true. Moreover, a Bernstein type theorem in the $3$-dimensional Minkowski space is established by considering the volume form induced from the projective sphere bundle.
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Additional Information
  • Qun He
  • Affiliation: Department of Applied Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
  • Email: hequn@mail.tongji.edu.cn
  • Yi-Bing Shen
  • Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310028, People’s Republic of China
  • Email: yibingshen@zju.edu.cn
  • Received by editor(s): June 4, 2004
  • Received by editor(s) in revised form: October 13, 2004
  • Published electronically: July 19, 2005
  • Additional Notes: The first author was supported in part by NNSFC (no.10471105).
    The second author was supported in part by NNSFC (no.10271106).
  • Communicated by: Richard A. Wentworth
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 871-880
  • MSC (2000): Primary 53C60; Secondary 53B40
  • DOI: https://doi.org/10.1090/S0002-9939-05-08017-2
  • MathSciNet review: 2180905