Abstract
Following closely the Laplace operator method of M. Gromov and V.D. Milman (1983), we slightly improve their general estimate of the concentration functionα(X; e) of a compact Riemannian manifold X by showing that α(X;e)≦C exp(−ce√ϱ0log(1+e√ϱ0)) for numerical constantsC, c > 0, whereρ 0 > 0 is the hypercontractive constant of the Laplacian onX.
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