完备黎曼流形上f指数调和型函数的梯度估计

doi:10.3969/j.issn.0253-2778.2015.09.002

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (9): 717-720.DOI: 10.3969/j.issn.0253-2778.2015.09.002

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完备黎曼流形上f指数调和型函数的梯度估计

邢杰

中国科学技术大学数学科学学院,安徽合肥 230026

收稿日期:2015-03-09 修回日期:2015-06-19 接受日期:2015-06-19 出版日期:2015-06-19 发布日期:2015-06-19

Gradient estimates for f-exponentially harmonic functions on complete Riemannian manifolds

XING Jie

School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

Received:2015-03-09 Revised:2015-06-19 Accepted:2015-06-19 Online:2015-06-19 Published:2015-06-19
About author:XING Jie, male, born in 1992, master. Research field: differential geometry in the large. E-mail:xj3553@mail.ustc.edu.cn

摘要/Abstract

摘要： 对于光滑的度量测度空间(M,g,e-fdvol),通过使用极大值原理，考虑了f指数调和型函数的梯度估计.当Bakry-Emery Ricci 张量非负并且截面曲率有负下界，可以得到刘维尔型定理.当f为常数时，即为文献[Wu J, Ruan Q, Yang Y H. Gradient estimate for exponentially harmonic functions on complete Riemannian manifolds. Manuscripta Mathematica, 2014, 143(3-4): 483-489]中的结果.

关键词: f指数调和型函数, 梯度估计, 刘维尔型定理

Abstract: For smooth metric measure spaces (M,g,e-fdvol), the gradient estimates of positive solutions to the f-exponentially harmonic functions was considered by using the maximum principle. Then a Liouville type theorem was obtained when the Bakry-Emery Ricci tensor was nonnegtive and the sectional curvature was bounded by a negative constant. This generalizes a result in Ref.[Wu J, Ruan Q, Yang Y H. Gradient estimates for exponentially harmonic functions on complete Riemannian manifolds. Manuscripta Mathematica, 2014, 143(3-4): 483-489], which is covered in the case where f is a constant.

Key words: f-exponentially harmonic function, gradient estimate, Liouville type theorem

中图分类号:

O186.1

邢杰. 完备黎曼流形上f指数调和型函数的梯度估计[J]. 中国科学技术大学学报, 2015, 45(9): 717-720.

XING Jie. Gradient estimates for f-exponentially harmonic functions on complete Riemannian manifolds[J]. Journal of University of Science and Technology of China, 2015, 45(9): 717-720.

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完备黎曼流形上f指数调和型函数的梯度估计

Gradient estimates for f-exponentially harmonic functions on complete Riemannian manifolds

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