On Hypersurfaces in Rn+1 with Bounds on Curvature

被引：12

作者：

Delladio, Silvano ^{[1
]}

机构：

[1] Univ Trent, Dipartimento Matemat, I-38050 Trento, Italy

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2001年 / 11卷 / 01期

关键词：

variational problems; direct method; functionals involving surfaces and curvatures; compactness for families of surfaces; hypersurfaces; immersions; generalized curvatures; bounded second fundamental form; Gauss graphs;

D O I：

10.1007/BF02921952

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the L P norm of the second fundamental form of hypersurfaces in Rn+1 is very coercive in the GMT setting of Gauss graphs currents, when p exceeds the dimension n. A compactness result for immersed hypersurfaces and its application to a variational problem are provided.

引用

页码：17 / 42

页数：26

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