Surveys in Differential Geometry

Volume 9 (2004)

From isoperimetric inequalities to heat kernels via symmetrization

Pages: 27 – 51



G. Besson (Institut Fourier, U.M.R. 5582 du C.N.R.S., Université de Grenoble I, B.P. 74, 38402 Saint Martin d’Hères Cedex, France)


We briefly describe the series of work that led from the Paul Lévy-Gromov isoperimetric inequality to the estimates on the heat kernel obtained by the technique of symmetrisation. An interpretation in terms of a spectral precompactness theorem is given at the end.

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