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 vector fields. Their
conjecture is proved in
a more general context using rearrangement techniques and
comparison manifolds.

Keywords: Rearrangements, Comparison Manifolds, Drift Vectorfields, Diffusions