A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS

doi:10.1007/s10473-024-0625-x

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (6): 2509-2526.doi: 10.1007/s10473-024-0625-x

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A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS

Xin HUANG^1,2

1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

收稿日期:2023-04-17 修回日期:2024-07-23 发布日期:2024-12-06
作者简介:Xin HUANG, E-mail: 17110180003@fudan.edu.cn; 003941@nuist.edu.cn
基金资助:
NSFC (11771087, 12171091).

A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS

Xin HUANG^1,2

1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
2. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received:2023-04-17 Revised:2024-07-23 Published:2024-12-06
About author:Xin HUANG, E-mail: 17110180003@fudan.edu.cn; 003941@nuist.edu.cn
Supported by:
NSFC (11771087, 12171091).

摘要/Abstract

摘要： In this paper, we prove a transversal $V$-Laplacian comparison theorem under a transversal Bakry-Emery Ricci condition. We establish a Schwarz type lemma for transversally $V$-harmonic maps of bounded generalized transversal dilatation between Riemannian foliated manifolds by using this comparison theorem, including for the case of $V = \nabla^{\mathcal{H}} h$.

关键词: Schwarz lemma, transversal $V$-Laplacian comparison theorem, transversally $V$-harmonic map

Abstract: In this paper, we prove a transversal $V$-Laplacian comparison theorem under a transversal Bakry-Emery Ricci condition. We establish a Schwarz type lemma for transversally $V$-harmonic maps of bounded generalized transversal dilatation between Riemannian foliated manifolds by using this comparison theorem, including for the case of $V = \nabla^{\mathcal{H}} h$.

Key words: Schwarz lemma, transversal $V$-Laplacian comparison theorem, transversally $V$-harmonic map

中图分类号:

53C12

Xin HUANG. A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS[J]. 数学物理学报(英文版), 2024, 44(6): 2509-2526.

Xin HUANG. A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS[J]. Acta mathematica scientia,Series B, 2024, 44(6): 2509-2526.

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A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS

A SCHWARZ LEMMA FOR TRANSVERSALLY $V$-HARMONIC MAPS BETWEEN RIEMANNIAN FOLIATED MANIFOLDS

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