叶状次椭圆调和映射的梯度估计——献给李工宝教授 70 寿辰

数学物理学报 ›› 2025, Vol. 45 ›› Issue (6): 1977-1984.

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叶状次椭圆调和映射的梯度估计——献给李工宝教授 70 寿辰

任益斌¹(), 陈钰莹¹(), 种田²^,^*()

¹浙江师范大学数学科学学院浙江金华 321004
²上海第二工业大学数理与统计学院上海 201209

收稿日期:2025-07-20 修回日期:2025-09-26 出版日期:2025-12-26 发布日期:2025-11-18
通讯作者: 种田 E-mail:allenryb@outlook.com;dyzl455@163.com;chongtian@sspu.edu.cn
作者简介:任益斌,E-mail:allenryb@outlook.com
陈钰莹,E-mail:dyzl455@163.com
基金资助:
国家自然科学基金(11223344)

Gradient Estimates for Foliated Subelliptic Harmonic Maps

Yibin Ren¹(), Yuying Chen¹(), Tian Chong²^,^*()

¹School of Mathematical Sciences, Zhejiang Normal University, Zhejiang Jinhua 321004
²School of Mathematics, Physics and Statistics, Shanghai Polytechnic University, Shanghai 201209

Received:2025-07-20 Revised:2025-09-26 Online:2025-12-26 Published:2025-11-18
Contact: Tian Chong E-mail:allenryb@outlook.com;dyzl455@163.com;chongtian@sspu.edu.cn
Supported by:
NSFC(11223344)

摘要/Abstract

摘要：

该文推导了叶状黎曼流形上黎曼距离函数的 sub-Laplacian 估计, 并将该结果应用于建立从完备非紧叶状黎曼流形到 Cartan-Hadamard 流形叶状次椭圆调和映射的梯度估计和 Liouville 型定理.

关键词: 叶状黎曼流形, 次椭圆调和映射, 梯度估计, Liouville 定理.

Abstract:

This paper derives the sub-Laplacian estimates of the Riemannian distance function on foliated Riemannian manifolds, and applies this result to establish the gradient estimates and Liouville-type theorems for foliated subelliptic harmonic maps from complete non-compact foliated Riemannian manifolds to Cartan-Hadamard manifolds. }

Key words: Riemannian foliations, subelliptic harmonic maps, gradient estimates, Liouville theorems.

中图分类号:

O186

任益斌, 陈钰莹, 种田. 叶状次椭圆调和映射的梯度估计——献给李工宝教授 70 寿辰[J]. 数学物理学报, 2025, 45(6): 1977-1984.

Yibin Ren, Yuying Chen, Tian Chong. Gradient Estimates for Foliated Subelliptic Harmonic Maps[J]. Acta mathematica scientia,Series A, 2025, 45(6): 1977-1984.

参考文献 14

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[12]	Chong T, Dong Y, Ren Y. Pseudo-harmonic maps from complete non-compact pseudo-Hermitian manifolds to regular balls. J Geom Anal, 2020, 30(4): 3512-3541 doi: 10.1007/s12220-019-00206-2
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叶状次椭圆调和映射的梯度估计——献给李工宝教授 70 寿辰

Gradient Estimates for Foliated Subelliptic Harmonic Maps

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