Quantitative gradient estimates for harmonic maps into singular spaces

2017/11/14 by Hui-Chun Zhang, Xiao Zhong, Zhang, Hui-Chun +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.05245

openalex publication_date 2017/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will show the Yau's gradient estimate for harmonic maps into a metric space (X,d_X) with curvature bounded above by a constant κ, κ≥0, in the sense of Alexandrov. As a direct application, it gives some Liouville theorems for such harmonic maps. This extends the works of S. Y. Cheng [4] and H. I. Choi [5] to harmonic maps into singular spaces.

Cited by

• Optimal boundary regularity of harmonic maps from RCD(K,N)-spaces to CAT(0)-spaces

Related

• Gradient estimate and Liouville theorems for p-harmonic maps
• Local Li-Yau's estimates on RCD^*(K,N) metric measure spaces
• Yau's gradient estimates on Alexandrov spaces
• Gradient estimates for weighted harmonic function with Dirichlet boundary condition
• Optimal estimates for the gradient of harmonic functions in the unit disk