Heat kernels and integral Ricci curvature bounds
- Christian Rose (TU Chemnitz, Germany)
Gaussian heat kernel bounds play a fundamental role in geometric analysis. We present recent results on explicit Gaussian upper bounds for non-compact manifolds depending on locally uniform Ricci curvature integral assumptions. Furthermore, we discuss generalizations of integral curvature bounds in terms of the so-called Kato class. If time allows, topological applications of those heat kernel upper bounds will be given.