论文标题
在Riemannian流行和Ricci流的香农熵功率上
On the Shannon entropy power on Riemannian manifolds and Ricci flow
论文作者
论文摘要
在本文中，我们证明了与Laplacian或Witten Laplacian相关的热方程式的香农熵功率的凹度，并在完整的Riemannian歧管上具有适当的曲率差异条件以及紧凑的Super Ricci流。在适当的曲率维度条件下，我们证明香农熵功率的刚性模型是带有黑森孤子的爱因斯坦或准爱因斯坦歧管。此外，我们证明了G. perelman在RICCI流程中引入的共轭热方程的香农熵功率的凸性，相应的刚度模型是Ricci solitons的收缩。作为一种应用，我们证明了具有非阴性（Bakry-Emery）RICCI曲率和最大体积生长条件的完整riemannian歧管上的熵等级不平等。
In this paper, we prove the concavity of the Shannon entropy power for the heat equation associated with the Laplacian or the Witten Laplacian on complete Riemannian manifolds with suitable curvature-dimension condition and on compact super Ricci flows. Under suitable curvature-dimension condition, we prove that the rigidity models of the Shannon entropy power are Einstein or quasi Einstein manifolds with Hessian solitons. Moreover, we prove the convexity of the Shannon entropy power for the conjugate heat equation introduced by G. Perelman on Ricci flow and that the corresponding rigidity models are the shrinking Ricci solitons. As an application, we prove the entropy isoperimetric inequality on complete Riemannian manifolds with non-negative (Bakry-Emery) Ricci curvature and the maximal volume growth condition.
