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Annals of Global Analysis and Geometry

, Volume 37, Issue 2, pp 113–124 | Cite as

Complete submanifolds in manifolds of partially non-negative curvature

  • Qiaoling WangEmail author
Original Paper

Abstract

We prove that a complete non-compact submanifold in a complete manifold of partially non-negative sectional curvature has only one end if the Sobolev inequality holds on it and if its total curvature is not very big by showing a Liouville theorem for harmonic maps and by using a existence theorem of constant harmonic functions with finite energy. We also generalize a result by Cao–Shen–Zhu saying that a complete orientable stable minimal hypersurface in a Euclidean space has only one end to submanifolds in manifolds of partially non-negative sectional curvature. Some related results about the structure of the same kind of submanifolds are also obtained.

Keywords

Liouville theorems Harmonic maps Submanifolds Total curvature 

Mathematics Subject Classification (2000)

53C20 53C42 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasíliaBrazil

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