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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
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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