The Li-Yau inequality and applications under a curvature-dimension condition
ANNALES DE L INSTITUT FOURIER(2017)
摘要
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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关键词
Li-Yau inequality,Harnack inequality,heat kernel bounds,Ricci curvature
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