# Large-time behavior of the heat kernel on manifolds with non-negative Ricci curvature

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David Tewodrose
(Université Libre de Bruxelles)

created by pluda on 11 May 2016

modified on 16 May 2016

18 may 2016
-- 17:30
[open in google calendar]

sala seminari, dipartimento di matematica di Pisa

**Abstract.**

The two formulae of the heat kernel on $\mathbb{R}^n$ and on the hyperbolic space$\mathbb{H}^n$ give a first example of the fact that the geometry of a space has an incidence on the heat kernel. On general manifolds, heat kernels are almost
never expressed by such explicit formulae. However, under some hypothesis
on the geometry of the manifold, nice upper or lower bounds of the heat
kernel can be obtained. In an article on 1986, P. Li used such bounds to
obtain a first result concerning the asymptotic behavior of the heat kernel
on manifolds with nonnegative Ricci curvature and maximal volume growth. In
2013, Xu obtained a similar result removing the maximal volume growth
hypothesis. The object of the seminar will be to present Li's and Xu's
works, stressing the use by Xu of Cheeger-Colding's theory.