Hypoelliptic heat kernel inequalities on H-type groups
Analysis of PDEs
2016-12-05 v3 Differential Geometry
Abstract
We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to derive an estimate on the gradient of solutions of the heat equation, which is known to have various significant consequences including logarithmic Sobolev inequalities. We also present a computation of the heat kernel, and a discussion of the geometry of H-type groups including their geodesics and Carnot-Carath\'eodory distance functions.
Cite
@article{arxiv.1406.1840,
title = {Hypoelliptic heat kernel inequalities on H-type groups},
author = {Nathaniel Eldredge},
journal= {arXiv preprint arXiv:1406.1840},
year = {2016}
}
Comments
Ph.D. dissertation, University of California, San Diego, 2009, 132 pages. Please read addendum at the beginning of the file for errata and updates