Isoperimetric control of the spectrum of a compact hypersurface
Metric Geometry
2014-09-17 v2
Abstract
Upper bounds for the eigenvalues of the Laplace-Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ratio of the domain. These results are applied to the extrinsic geometry of isometric embeddings.
Keywords
Cite
@article{arxiv.1007.0826,
title = {Isoperimetric control of the spectrum of a compact hypersurface},
author = {Bruno Colbois and Ahmad El Soufi and Alexandre Girouard},
journal= {arXiv preprint arXiv:1007.0826},
year = {2014}
}
Comments
To appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal)