次黎曼流形上的次椭圆调和映射梯度估计
Gradient Estimate of Subelliptic Harmonic Maps on Sub-Riemannnian Manifolds
DOI: 10.12677/AAM.2021.1011416, PDF, HTML,  被引量 下载: 258  浏览: 399 
作者: 邹文婷：浙江师范大学，数学与计算机科学学院，浙江 金华
关键词: 次黎曼流形；次椭圆调和映射；黎曼叶状结构；梯度估计；Liouville 定理；Sub-Riemannian Manifolds； Subelliptic Harmonic Maps； Riemannian Foliation； Gradient Estimate； Liouville’s Theorem
摘要: 如果黎曼叶状结构的水平分布满足括号生成条件，则它是—类特殊的次黎曼流形。本文主要研究此类黎曼叶状结构上次椭圆调和映射的梯度估计及Liouville 定理。
Abstract: The Riemannian foliation is a special class of sub-Riemannian manifolds, if its hori-zontal distribution satisfies the bracket generating condition. In this paper, we study the gradient estimation of the subelliptic harmonic maps and the Liouville-type theorems.
文章引用：邹文婷. 次黎曼流形上的次椭圆调和映射梯度估计[J]. 应用数学进展, 2021, 10(11): 3912-3922. https://doi.org/10.12677/AAM.2021.1011416

参考文献

[1] Yau, S. (1975) Harmonic Functions on Complete Riemannian Manifolds. Communications on Pure and Applied Mathematics, 28, 201-228.
https://doi.org/10.1002/cpa.3160280203
[2] Cheng, S.Y. (1980) Liouville Theorem for Harmonic Maps. Proceedings of Symposia in Pure Mathematics, 36, 147-151.
https://doi.org/10.1090/pspum/036/573431
[3] Choi, H.I. (1982) On the Liouville Theorem for Harmonic Maps. Proceedings of the American Mathematical Society, 85, 91-94.
https://doi.org/10.1090/S0002-9939-1982-0647905-3
[4] Strichartz, R.S. (1986) Sub-Riemannian Geometry. Journal of Differential Geometry, 24, 221- 263.
https://doi.org/10.4310/jdg/1214440436
[5] Dong, Y. (2021) Eells-Sampson Type Theorems for Subelliptic Harmonic Maps from Sub- Riemannian Manifolds. Journal of Geometric Analysis, 31, 3608-3655.
https://doi.org/10.1007/s12220-020-00408-z
[6] Baudoin, F. (2016) Sub-Laplacians and Hypoelliptic Operators on Totally Geodesic Rieman- nian Foliations. Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds, 259-321.
https://doi.org/10.4171/162-1/3
[7] Chong, T., Dong, Y.X., Ren, Y.B., et al. (2020) Pseudo-Harmonic Maps from Complete Non- compact Pseudo-Hermitian Manifolds to Regular Balls. Journal of Geometric Analysis, 30, 3512-3541.
https://doi.org/10.1007/s12220-019-00206-2

为你推荐