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arXiv · 1307.2326

Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators

Bin Qian
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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 Schödinger 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.

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Bin Qian. 2013-07-09. Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators. https://arxiv.org/abs/1307.2326

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