In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci s...In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.展开更多
本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,...本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,热方程的正解u (x, t)的最优Li-Yau梯度估计。In this paper, the problem of Li-Yau gradient estimation of weighted Laplace operator under Bakry-Émery Ricci curvature is studied. Bochner formula, weighted Laplace formula and the maximum theorem are used to deal with the Li-Yau gradient problem. The optimal Li-Yau gradient estimation for the positive solution u (x, t) of the heat equation is obtained under the condition of lower bound for weighted Laplace Bakry-Émery Ricci curvature.展开更多
基金Supported by NSFC(Nos.12371051,12141101,11871126)。
文摘In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.
基金Supported by the National Natural Science Foundation of China(11371386)the European Union’s Seventh Framework Programme(FP7/2007-2013)under grant agreement(317721)
文摘本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,热方程的正解u (x, t)的最优Li-Yau梯度估计。In this paper, the problem of Li-Yau gradient estimation of weighted Laplace operator under Bakry-Émery Ricci curvature is studied. Bochner formula, weighted Laplace formula and the maximum theorem are used to deal with the Li-Yau gradient problem. The optimal Li-Yau gradient estimation for the positive solution u (x, t) of the heat equation is obtained under the condition of lower bound for weighted Laplace Bakry-Émery Ricci curvature.
