Calculus of Variations and Geometric Measure Theory
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S. Delladio

On hypersurfaces in $R^{n+1}$ with integral bounds on curvature

created on 14 Dec 2001


Published Paper

Inserted: 14 dec 2001

Journal: J. Geom. Anal.
Volume: 11
Pages: 17-41
Year: 2000


We show that the $L^p$ norm of the second fundamental form of hypersurfaces in $R^{n+1}$ is very cohercive 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.

Keywords: Variational problems, generalized curvature, direct method, compactness for families of surfaces

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