Volume et courbure totale pour les hypersurfaces de l'espace euclidien
微分几何
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0212302,
title = {Volume et courbure totale pour les hypersurfaces de l'espace euclidien},
author = {Alexandru Oancea},
journal= {arXiv preprint arXiv:math/0212302},
year = {2007}
}
备注
36 pages, 4 figures