A method of symmetrization ; Applications to heat and spectral estimates
A mean-value lemma and applications
We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write...
The Hodge laplacian on manifolds with boundary
Estimates of the heat content on a class of domains.
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