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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A simple analytic proof of an inequality by P. Buser


Author: M. Ledoux
Journal: Proc. Amer. Math. Soc. 121 (1994), 951-959
MSC: Primary 53C21; Secondary 58G25
DOI: https://doi.org/10.1090/S0002-9939-1994-1186991-X
MathSciNet review: 1186991
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1186991-X
Article copyright: © Copyright 1994 American Mathematical Society