The Li-Yau inequality and applications under a curvature-dimension condition
The Li-Yau inequality and applications under a curvature-dimension condition
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DOI：
10.5802/aif.3086
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
D. Bakry;Franccois Bolley;I. Gentil
中科院分区：
文献类型：
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作者：
D. Bakry;Franccois Bolley;I. Gentil
在曲率维数条件下证明了一般马氏半群的一个整体Li-Yau不等式。这个不等式比我们已知的所有经典的Li-Yau型不等式都强。在黎曼流形上，它等价于一个新的抛物Harnack不等式，在负曲率和正曲率下，给出了半群热核的新的一致性界。在正曲率下，我们还通过一种直接而鲁棒的方法达到了超压缩的界限。
We prove a global Li-Yau inequality for a general Markov semigroup 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 subsequents bounds on the heat kernel of the semigroup. Under positive curvature we moreover reach ultracontractive bounds by a direct and robust method.