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Volume et courbure totale pour les hypersurfaces de l'espace euclidien

Alexandru Oancea
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Abstract

The paper investigates higher dimensional analogues of Burago's inequality bounding the area of a closed surface by its total curvature. We obtain sufficient conditions for hypersurfaces in 4-space that involve the Ricci curvature. We get semi-local variants of the inequality holding in any dimension that involve domains with non-vanishing Gauss-Kronecker curvature. The paper also contains inequalities of isoperimetric type involving the total curvature, as well as a "reverse" isoperimetric inequality for spaces with constant curvature.

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Alexandru Oancea. 2002-12-21. Volume et courbure totale pour les hypersurfaces de l'espace euclidien. https://arxiv.org/abs/math/0212302

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