Heat kernels on Riemannian manifolds
Tuesday, 27 March, 2018 - 14:00 - 16:00
Prof. Alexander GRIGOR'YAN
Universität Bielefeld, Germany
The course is devoted to the heat equation and heat kernel on arbitrary Riemannian manifolds. The following topics will be considered.
- Cauchy problem for the heat equation: uniqueness classes.
- Stochastic completeness: equivalent conditions and volume test.
- Long time behaviour of the heat kernel and isoperimetric properties.
- Heat kernel bounds and volume growth.
- Escape rate of Brownian motion on manifolds with polynomial volume growth.