A Simple Analytic Proof of an Inequality by P. Buser
- 1 July 1994
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 121 (3) , 951-959
- https://doi.org/10.2307/2160298
Abstract
We present a simple analytic proof of the inequality of P. Buser showing the equivalence of the first eigenvalue of a compact Riemannian manifold without boundary and Cheeger's isoperimetric constant under a lower bound on the Ricci curvature. Our tools are the Li-Yau inequality and ideas of Varopoulos in his functional approach to isoperimetric inequalities and heat kernel estimates on groups and manifolds. The method is easily modified to yield a logarithmic isoperimetric inequality involving the hypercontractivity constant of the manifold.Keywords
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