A simple analytic proof of an inequality by P. Buser
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- by M. Ledoux
- Proc. Amer. Math. Soc. 121 (1994), 951-959
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186991-X
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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.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- 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