Metric shape of hypersurfaces with small extrinsic radius or large $ λ_1$

Erwann Aubry; Jean-Francois Grosjean

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arXiv · 1210.5689

Metric shape of hypersurfaces with small extrinsic radius or large $ λ_1$

Erwann Aubry·Jean-Francois Grosjean

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Abstract

We determine the Hausdorff limit-set of the Euclidean hypersurfaces with large $λ_1$ or small extrinsic radius. The result depends on the $L^p$ norm of the curvature that is assumed to be bounded a priori, with a critical behaviour for $p$ equal to the dimension minus 1.

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BibTeX RIS

Erwann Aubry, Jean-Francois Grosjean. 2012-10-21. Metric shape of hypersurfaces with small extrinsic radius or large $ λ_1$. https://arxiv.org/abs/1210.5689

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