Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators
Differential Geometry
2013-07-10 v1 Analysis of PDEs
Abstract
In this paper, under the generalized curvature-dimension inequality recently introduced by F. Baudoin and N. Garofalo, we obtain differential Harnack inequalities for the positive solutions to the Sch\"odinger equation associated to subelliptic operator with potential. As applications of the differential Harnack inequality, we derive the corresponding parabolic Harnack inequality. Also we define the Perelman type entropy associated to subelliptic operators and derive its monotonicity.
Keywords
Cite
@article{arxiv.1307.2326,
title = {Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators},
author = {Bin Qian},
journal= {arXiv preprint arXiv:1307.2326},
year = {2013}
}
Comments
15 pages, 0 figures. Any comment are welcomed