黎曼流形中完备极小超曲面的端
The End of a Complete Minimal Hypersurface in Riemannian Manifold
DOI: 10.12677/PM.2013.36057, PDF, HTML, 下载: 3,203  浏览: 7,623  国家自然科学基金支持
作者: 刘 露, 陈抚良：江西师范大学数学与信息科学学院，南昌
关键词: 极小超曲面；端；第一特征值；Minimal Hypersurface; End; The First Eigenvalue
摘要: 本文研究了黎曼流形中完备非紧致非全测地极小超曲面的端。在一定的条件下，我们得出这种超曲面只有一个端。
Abstract: In this paper, we study the end of a complete noncompact non-totally geodesic minimal hypersurface. Under certain conditions, we obtain that the hypersurface has only one end.
文章引用：刘露, 陈抚良. 黎曼流形中完备极小超曲面的端[J]. 理论数学, 2013, 3(6): 374-378. http://dx.doi.org/10.12677/PM.2013.36057

参考文献

[1] Dung, N.T. and Seo, K. (2012) Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature. Annals of Global Analysis and Geometry, 41, 447-460.
[2] Tam, L.F. and Zhou, D.T. (2009) Stability properties for the higher dimensional Catenoid in Rn+1. American Mathematical Society, 137, 3451-3461.
[3] Neto, N.M.B. and Wang, Q.L. (2012) Some Bernstein-type Rigidity theorems. Journal of Mathematical Analysis and Applications, 389, 694-700.
[4] Leung, P.F. (1992) An estimate on the Ricci curvature of a submanifold and some applications. Proceedings of the American Mathematical Society, 114, 1051-1063.
[5] Wang, X. (2001) On conformally compact Einstein manifolds. Mathematical Research Letters, 8, 671-688.
[6] Seo, K. (2010) L2 harmonic 1-forms on minimal submanifolds in hyperbolic Space. Journal of Mathematical Analysis and Applications, 371, 546-551.
[7] Seo, K. (2010) Rigidity of minimal submanifolds in hyperbolic space. Archiv der Mathematik, 94, 173-181.
[8] Wei, S.W. (2003) The structure of complete minimal submanifolds in complete manifolds of nonpositive curvature. Houston Journal of Mathematics, 29, 675-689.

为你推荐