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.

引用

页码：81 / 145

页数：65

共 50 条

[31] Cross-invariant manifolds for the Gross-Pitaevskii-Poisson equation
Zhou, Xiaoyu
Zhu, Shihui
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (04):
[32] Solvability of the Dirichlet Problem for the Poisson Equation on Some Noncompact Riemannian Manifolds
Losev, A. G.
DIFFERENTIAL EQUATIONS, 2017, 53 (12) : 1595 - 1604
[33] Solvability of the Dirichlet Problem for the Poisson Equation on Some Noncompact Riemannian Manifolds
A. G. Losev
Differential Equations, 2017, 53 : 1595 - 1604
[34] Hermitian-Poisson Metrics on Flat Bundles over Complete Hermitian Manifolds
Pan, Changpeng
CHINESE ANNALS OF MATHEMATICS SERIES B, 2021, 42 (04) : 575 - 582
[35] Hermitian-Poisson Metrics on Flat Bundles over Complete Hermitian Manifolds
Changpeng PAN
ChineseAnnalsofMathematics,SeriesB, 2021, (04) : 575 - 582
[36] Hermitian-Poisson Metrics on Flat Bundles over Complete Hermitian Manifolds
Changpeng Pan
Chinese Annals of Mathematics, Series B, 2021, 42 : 575 - 582
[37] Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds
Chen, Daguang
Li, Haizhong
Wei, Yilun
INTERNATIONAL JOURNAL OF MATHEMATICS, 2023, 34 (08)
[38] POISSON COHOMOLOGY OF REGULAR POISSON MANIFOLDS
XU, P
ANNALES DE L INSTITUT FOURIER, 1992, 42 (04) : 967 - 988
[39] Some remarks on the prescribed mean curvature equation on complete manifolds
Pigola, S
Rigoli, M
Setti, AG
PACIFIC JOURNAL OF MATHEMATICS, 2002, 206 (01) : 195 - 217
[40] Heat equation for harmonic maps between complete Riemannian manifolds
Fardoun, A
Regaboui, R
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (04): : 299 - 304

← 1 2 3 4 5 →