Daniel Lenz (Jena)

Large time behaviour of heat kernels

Abstract: We study long time behaviour of heat kernels and show convergence of the semigroup to the ground state and convergence of suitably averaged logarithms of kernels to the ground state energy. The results hold for arbitrary selfadjoint positivity improving semigroups. This framework includes Laplace operator on manifolds, on graphs and on quantum graphs. (Joint work with Matthias Keller, Hendrik Vogt, Radoslaw Wojciechowski)