光滑度量空间上熵的渐进估计

Asymptotic estimates for the entropy on smooth metric measure spaces

在Bakry-émery曲率有下界的闭光滑度量测度空间上给出了加权Nash熵以及Perelman的加权W-熵随着时间演化的渐进估计,还借助于加权Laplace算子的第一非零特征值得到了加权Nash熵的一个精细估计。这些结果是Ni的关于Nash熵以及Perelman的W-熵演化公式的深化。

In this paper,we give asymptotic estimates evolving along the time for the weighted Nash's entropy and Perelman's W-entropy on closed smooth metric measure spaces with the Bakry-émery curvature bounded from below;we also get refined asymptotic estimates by the first nonzero eigenvalue of the weighted Laplacian.All these results deepen the evolving formulas for the Nash’s entropy and Perelman’s W-entropy established by Ni.