渐进非负曲率流形的Poisson方程解的估计  

A sharp estimate on the solution of Poisson equation of asymptotically nonnegative curvature

作　　者：赵成兵[1] 

机构地区：[1]安徽建筑工业学院数学系,安徽合肥230022

出　　处：《合肥工业大学学报（自然科学版）》2011年第4期631-633,共3页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校自然科学基金重点资助项目(KJ2011A061);安徽省自然科学基金资助项目(11040606M01);安徽建筑工业学院博士基金资助项目(2007-6-3)

摘　　要：M为完备非紧的Khler流形有非负的全纯双截曲率和极大体积增长且数量曲率二次退化的条件下,可以通过研究Poisson方程来解Poincaré-Lelong方程,并应用Poincaré-Lelong方程研究和分析流形M的几何性质,文章主要研究了完备非紧非抛物的有渐近非负曲率n维Khler流形M的Poisson方程的解的估计,得到几个解的估计表达式。As M is a complete noncompact Khler manifold with nonnegative holomorphic bisectional curvature and has maximal volume growth,and scalar curvature decays twice,the Poincaré-Lelong equations can be solved by the solution of Poisson equation and the result can be applied to studying the geometric properties of M manifold.In this paper,the sharp estimates on the solutions of Poisson equation of complete noncompact nonparabolic n-dimensional Khler manifold with asymptotically nonnegative curvature are researched,and some expressions of the sharp estimates are obtained.

关 键 词：渐近非负曲率流形 POISSON方程 解的估计 

分 类 号：O186.1[理学—数学]