Brice Franke
Heat Content Inequalities for Diffusions on Manifolds
Preprint series: Mathematica Gottingensis

MSC:

58G11 Heat and other parabolic equation methods

47D07 Markov semigroups

Abstract: The main Purpose of this thesis is to prove a conjecture of
Bhattacharya and Goetze which arose from their research on
central limit theorems for diffusions with periodic drift
vectorfields. Their conjecture is proved in a more general
context using comparison manifolds and rearrangement
techniques.
Keywords: Comparison Manifolds, Rearrangements, Drift Vectorfields, Heat Propagation