On hypersurfaces in \(\mathbb{R}^{n+1}\) with integral bounds on curvature.

DOI10.1007/BF02921952zbMath1034.49043OpenAlexW2036101829MaRDI QIDQ5950187

Silvano Delladio

Publication date: 9 October 2002

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921952

zbMATH Keywords

integral bounds on curvature

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05)

Related Items (6)

Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs ⋮ First variation formula for generalized Gauss graphs ⋮ A sufficient condition for the \(C^H\)-rectifiability of Lipschitz curves ⋮ Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces ⋮ $C^1$-regularity for local graph representations of immersions ⋮ Immersions with bounded second fundamental form

Cites Work

• A compactness theorem for surfaces with \(L_ p\)-bounded second fundamental form
• Poincaré-Sobolev and related inequalities for submanifolds of \(R^ n\)
• Curvature varifolds with boundary
• Surfaces with generalized second fundamental form in \(L^ 2\) are Lipschitz manifolds
• Minimizing functionals depending on surfaces and their curvatures: A class of variational problems in the setting of generalized Gauss graphs
• Area and the area formula
• Special generalized Gauss graphs and their application to minimization of functional involving curvatures.
• Oriented and nonoriented curvature varifolds
• Slicing of generalized surfaces with curvature measures and diameter's estimate
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