HARMONIC FUNCTIONS ON A COMPLETE NONCOMPACT MANIFOLD WITH ASYMPTOTICALLY NONNEGATIVE CURVATURE 被引量：5

HARMONIC FUNCTIONS ON A COMPLETE NONCOMPACT MANIFOLD WITH ASYMPTOTICALLY NONNEGATIVE CURVATURE

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摘要 The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.

作者 ZHOUCHAOHUI CHENZHIHUA

机构地区 DepartmentofAppliedMathematics

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第4期523-532,共10页 数学年刊（B辑英文版）

基金 Project supported by the National Natural Science Foundation of China (No.10271089).

关键词 Harmonic function Asymptotically nonnegative curvature Polynomial growth 谐函数渐近线正曲率多项式级数黎曼流形

分类号 O189.31 [理学—基础数学]

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参考文献4

1[1]Colding, T. H. & Minicozzi Ⅱ, W. P., Harmonic function on manifolds, Ann. Math., 146(1997), 725-747.
2[2]Yau, S. T., Some function theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. J., 25(1976), 659-670.
3[3]Gromov, M., Curvature, diameter and Betti numbers, Comment. Math. Hel., 56(1981), 179-195.
4[4]Buser, P., A note on the isoperimetric constant, Ann. Scient. Ec. Norm. Sup., 15(1982), 213-230.

同被引文献4

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2NI Lei,SHI Yuguan,TAM Luenfai.Poisson equation,PoincaréLelong equation and decay on complete K(a)hler manifold[J].Differential Geometry,2001,57:339.
3CHENG S Y,YAU S T.Differential equation on Rimannian manifold and their geometric application[J].Comm Pure Apply Math,1975,28:333.
4赵成兵,俞能福.一个关于Khler平坦的定理[J].合肥工业大学学报（自然科学版）,2008,31(9):1528-1531. 被引量：1

引证文献5

1阮其华,蔡娜.流形上的调和函数空间[J].漳州师范学院学报（自然科学版）,2005,18(2):13-17.
2赵成兵.渐进非负曲率流形上的函数[J].佳木斯大学学报（自然科学版）,2005,23(3):335-337.
3赵成兵,阮其华.关于Poisson方程解的一个注记[J].同济大学学报（自然科学版）,2006,34(5):694-697. 被引量：1
4周朝晖.曲率渐近非负流形[J].数学年刊（A辑）,2006,27(3):395-404.
5赵成兵.渐进非负曲率流形的Poisson方程解的估计[J].合肥工业大学学报（自然科学版）,2011,34(4):631-633.

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1赵成兵.渐进非负曲率流形的Poisson方程解的估计[J].合肥工业大学学报（自然科学版）,2011,34(4):631-633.

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3邵剑.时滞系统问题的一种近似解方法[J].浙江大学学报（自然科学版）,1997,31(1):28-35. 被引量：1
4Arturo Fernández,Javier Pérez.ON A CLASS OF RIEMANN SURFACES[J].Analysis in Theory and Applications,2006,22(4):377-386.
5ZHOU ChaoHui,CHEN ZhiHua.L-harmonic functions with polynomial growth of a fixed rate[J].Science China Mathematics,2009,52(12):2855-2862.
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8XIE Wen-Fang.Three Charged Bosons Confined in a Harmonic Trap[J].Communications in Theoretical Physics,2005,44(3X):529-531.
9陈乃辉.条件数学期望及随机变量函数的三角多项式级数展开[J].四川师范大学学报（自然科学版）,2007,30(5):551-555.
10李声锋,陈栋栋.连分式的逼近计算及其Mathematica实现[J].重庆科技学院学报（自然科学版）,2015,17(4):122-124.

Chinese Annals of Mathematics,Series B

2004年第4期

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HARMONIC FUNCTIONS ON A COMPLETE NONCOMPACT MANIFOLD WITH ASYMPTOTICALLY NONNEGATIVE CURVATURE 被引量：5

参考文献4

同被引文献4

引证文献5

二级引证文献1

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