Equivalent Harnack and gradient inequalities for pointwise curvature lower bound |
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| Authors: | Marc Arnaudon Anton Thalmaier Feng-Yu Wang |
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| Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;2. Institut de Mathématiques de Bordeaux, UMR 5251 Université de Bordeaux and CNRS, France;3. Mathematics Research Unit, FSTC, University of Luxembourg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg;4. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, United Kingdom |
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| Abstract: | By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) diffusion semigroups on a Riemannian manifold (possibly with boundary). This inequality as well as the consequent L2-gradient inequality, are proved to be equivalent to the pointwise curvature lower bound condition together with the convexity or absence of the boundary. Some applications of the log-Harnack inequality are also introduced. |
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| Keywords: | 58J65 60H30 |
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