, Volume 11, Issue 1, pp 17-42

On hypersurfaces inR n+1 with integral bounds on curvature

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We show that the L p norm of the second fundamental form of hypersurfaces in R n+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.