紧致黎曼流形上对数热核的高阶导数估计  

The Estimate of Higher Derivatives of Logarithmic Heat Kernel on Compact Riemannian Manifold

作　　者：时颖慧 苗苗 SHI Yinghui;MIAO Miao(School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou,221116,China)

机构地区：[1]江苏师范大学数学与统计学院,徐州221116

出　　处：《应用概率统计》2018年第3期265-274,共10页Chinese Journal of Applied Probability and Statistics

基　　金：江苏省高校优势学科统计学及江苏省高校自然科学研究面上项目(批准号:16KJB110006)资助

摘　　要：设M为一个d-维紧致黎曼流形,对任意的t∈(0,1],x,y∈M,记pM(t,x,y)是M的极小热核.本文利用流形M上的水平布朗桥,把文献[1]中关于对数热核lnpM(t,x,y)的单变量的高阶导数估计推广到关于(x,y)两个变量上,即对于任意的非负整数n,m,都存在依赖于n,m和流形M的常数C使得下式成立:|▽_x^n▽_y^mlnpM(t,x,y)|≤C[d(x,y)/t+1/t^(1/2)]^(n+m).Let pM(t,x,y)be the minimal heat kernel of a d-dimenional compact Riemannian manifold M for any time t∈(0,1]and x,y∈M.Using the horizontal Brown bridge on M,we prove that,for any nonnegative integers n and m,there is a constant C depending on n;m and the manifold M,such that|▽x^n▽y^m lnpM(t,x,y)|≦C[d(x,y)/t+1/√t]^n+m,which generalizes the conclusion of the higher derivatives of the logarithmic heat kernel ln pM(t,x,y)about single variable in[1].

关 键 词：紧致黎曼流形 对数热核 水平布朗桥 高阶导数 

分 类 号：O211.6[理学—概率论与数理统计]