Heat kernel upper bounds under the generalized curvature(-dimension) inequality
Mathematical Physics
2013-08-29 v1 math.MP
Abstract
In the sub-Riemannian manifolds, on the one hand, following Baudoin-Garofalo \cite{BaudoinGarofalo}, the upper bound for heat kernels associated to a class of locally subelliptic operators are given under the generalized curvature-dimension inequality with a negative curvature parameter; on the other hand, the argument combining Grigor'yan's integrated maximum principle with Wang's dimension-free Harnack inequality is also shown to derive the upper bound for the heat kernel under the generalized curvature inequality.
Cite
@article{arxiv.1308.6131,
title = {Heat kernel upper bounds under the generalized curvature(-dimension) inequality},
author = {Huai Qian LI},
journal= {arXiv preprint arXiv:1308.6131},
year = {2013}
}