A universal bound on the gradient of logarithm of the heat kernel for manifolds with bounded Ricci curvature

被引：14

作者：

Engoulatov, A. ^{[1
]}

机构：

[1] Univ Paris 11, Math Lab, F-91405 Orsay, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2006年 / 238卷 / 02期

关键词：

Ricci curvature; diffusion process; heat kernel; gradient estimate;

D O I：

10.1016/j.jfa.2006.02.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive a gradient estimate for the logarithm of the heat kernel on a Riemannian manifold with Ricci curvature bounded from below. The bound is universal in the sense that it depends only on the lower bound of Ricci curvature, dimension and diameter of the manifold. Imposing a more restrictive non-collapsing condition allows one to sharpen this estimate for the values of time parameter close to zero. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：518 / 529

页数：12

共 7 条

[1]

Bakry D, 1999, REV MAT IBEROAM, V15, P143

[2]

Bakry D., 1985, LECT NOTES MATH, V1123, P177, DOI DOI 10.1007/BFB0075847

[3]

Hsu E., 2002, GRAD STUD MATH, V38

[4] Estimates of derivatives of the heat kernel on a compact Riemannian manifold [J].