Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces
Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces
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RCD(0, N) 空间上 W 熵的单调性和刚性
DOI：
10.1007/s00229-019-01177-y
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Xiang-Dong Li
中科院分区：
文献类型：
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作者：
Kazumasa Kuwada;Xiang-Dong Li
利用时空Wasserstein控制，在适当的意义下，证明了具有非负Ricci曲率和有限维数上界的可能奇异度量测度空间上W-熵泛函在时间上沿着热流的单调性.还证明了关于W-熵耗散率的相关刚性结果。这些结果在某些方面甚至推广了加权黎曼流形上的已知结果。此外，我们还揭示了在光滑加权黎曼流形类中，某些奇异空间将表现刚性模型，而只有欧氏空间才表现刚性模型。
By means of a space-timeWasserstein control, we show the monotonicity of the.W-entropy functional in time along heat flows on possibly singular metric measure spaces.with non-negative Ricci curvature and a finite upper bound of dimension in an appropriate.sense. The associated rigidity result on the rate of dissipation of theW-entropy is also proved..These extend known results even on weighted Riemannian manifolds in some respects. In.addition, we reveal that some singular spaces will exhibit the rigidity models while only the.Euclidean space does in the class of smooth weighted Riemannian manifolds.