调和Ricci流下热方程的梯度估计及应用  

The gradient estimation of heat equation and its application under the harmonic-Ricci flow

作　　者：赵润柯 桂湘 方守文[1] ZHAO Runke;GUI Xiang;FANG Shouwen(School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2023年第5期15-21,共7页Journal of Yangzhou University：Natural Science Edition

基　　金：江苏省自然科学基金资助项目(BK20191435);扬州大学创新培育基金资助项目(2019CXJ002)。

摘　　要：在度量满足调和Ricci流的闭黎曼流形上,利用抛物型方程的极值原理证明热方程正解的一个梯度估计.结合索伯列夫不等式和指数加权法,进一步得到共轭热方程基本解的高斯型上界.On a closed Riemannian manifold with a harmonic-Ricci flow,a gradient estimation of the positive solution of the heat equation is proved by using the extreme value principle of the parabolic equation.The Gaussian type upper bound for the fundamental solutions of the conjugate heat equation is further obtained with the help of Sobolev inequality and the exponential weighting method.

关 键 词：调和Ricci流 梯度估计 热方程 共轭热方程 基本解 

分 类 号：O186.12[理学—数学]