Surveys in Differential Geometry
Volume 9 (2004)
From isoperimetric inequalities to heat kernels via symmetrization
Pages: 27 – 51
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.