Poisson equation on complete manifolds

被引：17
|
作者：
Munteanu, Ovidiu [1 ]
Sung, Chiung-Jue Anna [2 ]
Wang, Jiaping [3 ]
机构：
[1] Univ Connecticut, Dept Math, Storrs, CT 06268 USA
[2] Natl Thing Hua Univ, Dept Math, Hsinchu, Taiwan
[3] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
来源：
ADVANCES IN MATHEMATICS | 2019年 / 348卷
关键词：
Poisson equation; Green's function; Bottom spectrum; Steady Ricci solitons; POINCARE-LELONG EQUATION; GREEN-FUNCTIONS; CURVATURE; LAPLACIAN; GEOMETRY; SPACES;
D O I：
10.1016/j.aim.2019.03.019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop heat kernel and Green's function estimates for manifolds with positive bottom spectrum. The results are then used to establish existence and sharp estimates of the solution to the Poisson equation on such manifolds with Ricci curvature bounded below. As an application, we show that the curvature of a steady gradient Ricci soliton must decay exponentially if it decays faster than linear and the potential function is bounded above. (C) 2019 Elsevier Inc. All rights reserved.
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页码：81 / 145
页数：65
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