The Journal of Geometric Analysis

, Volume 11, Issue 1, pp 17–42

On hypersurfaces inRn+1 with integral bounds on curvature

Article

DOI: 10.1007/BF02921952

Cite this article as:
Delladio, S. J Geom Anal (2001) 11: 17. doi:10.1007/BF02921952

Abstract

We show that the Lpnorm of the second fundamental form of hypersurfaces inRn+1is 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.

Math Subject Classifications

49J4549Q1549Q2053C4249Q1053A0553C6553C21

Key Words and Phrases

variational problemsdirect methodfunctionals involving surfaces and curvaturescompactness for families of surfaceshypersurfacesimmersionsgeneralized curvaturesbounded second fundamental formGauss graphs

Copyright information

© Mathematica Josephina, Inc. 2001

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoPovo, TrentoItaly