从Finsler流形到Riemann流形的调和映射梯度估计
Gradient Estimate for Harmonic Maps from Finsler Manifolds to Riemannian Manifolds
摘要:
本文主要研究了从Finsler流形到Riemann流形的调和映射的梯度估计，并由此得到从弱Landsberg流形到Cartan-Hadamard流形的调和映射Liouville型定理。此外，我们还将这一定理推广至目标流形为正则球的情形。
Abstract:
In this paper, we study gradient estimate for harmonic maps from Finsler manifolds to Riemannian manifolds. As an application, we obtain Liouville type theorem of harmonic maps from a weak Landsberg manifold to a Cartan-Hadamard manifold. Moreover, we generalize the Liouville type theorem to a regular ball of Riemannian manifold.
文章引用：范振海, 任益斌. 从Finsler流形到Riemann流形的调和映射梯度估计[J]. 理论数学, 2020, 10(2): 80-90.
参考文献
|
[1]
|
Yau, S. (1975) Harmonic Functions on Complete Riemannian Manifolds. Communications on Pure and Applied Mathematics, 28, 201-228. [Google Scholar] [CrossRef]
|
|
[2]
|
Cheng, S. (1980) Liouville Theorem for Harmonic Maps. Proceedings of Symposia in Pure Mathematics, 36, 147-151. [Google Scholar] [CrossRef]
|
|
[3]
|
Choi, H. (1982) On the Liouville Theorem for Harmonic Maps. Proceeding of the American Mathematical Society, 85, 91-94. [Google Scholar] [CrossRef]
|
|
[4]
|
Xia, C. (2014) Local Gradient Estimate for Harmonic Functions on Finsler Manifolds. Calculus of Variations and Partial Differential Equations, 51, 849-865. [Google Scholar] [CrossRef]
|
|
[5]
|
Ohta, S. and Sturm, K. (2014) Bochner-Weitzenb?ck Formula and Li-Yau Estimates on Finsler Manifolds. Advances in Mathematics, 252, 429-448. [Google Scholar] [CrossRef]
|
|
[6]
|
Cheng, S. and Yau, S. (1975) Differential Equations on Riemannian Manifolds and Their Geometric Applications. Communications on Pure and Applied Mathematics, 28, 333-354. [Google Scholar] [CrossRef]
|
|
[7]
|
莫小欢. 黎曼-芬斯勒几何基础[M]. 北京: 北京大学出版社, 2007: 35-120.
|
|
[8]
|
Shen, Y.B. and Zhang, Y. (2004) Second Variation of Harmonic Maps between Finsler Manifolds. Science China-mathematics, 4, 39-51. [Google Scholar] [CrossRef]
|
|
[9]
|
沈一兵, 沈忠民. 现代芬斯勒几何初步[M]. 北京: 高等教育出版社, 2013: 21-25.
|
|
[10]
|
贺群, 尹松庭, 赵玮. Finsler调和映射与Laplace算子[M]. 北京: 科学出版社, 2014: 24-26.
|
|
[11]
|
Mo, X.H. (2001) Harmonic Maps from Finsler Manifolds. Illinois Journal of Mathematics, 45, 1331-1345. [Google Scholar] [CrossRef]
|