期刊
ANNALES DE L INSTITUT FOURIER
卷 67, 期 1, 页码 397-421出版社
ANNALES INST FOURIER
DOI: 10.5802/aif.3086
关键词
Li-Yau inequality; Harnack inequality; heat kernel bounds; Ricci curvature
类别
资金
- French STAB project [ANR-12-BS01-0019]
We prove a global Li-Yau inequality for a general Markov semi group under a curvature-dimension condition. This inequality is stronger than all classical Li-Yau type inequalities known to us. On a Riemannian manifold, it is equivalent to a new parabolic Harnack inequality, both in negative and positive curvature, giving new subsequent bounds on the heat kernel of the semigroup. Under positive curvature we moreover reach ultracontractive bounds by a direct and robust method.
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