黎曼流形中完备极小超曲面的端
The End of a Complete Minimal Hypersurface in Riemannian Manifold

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 (2013) 黎曼流形中完备极小超曲面的端。 理论数学, 3, 374-378. doi: 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.

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