Quantitative gradient estimates for harmonic maps into singular spaces

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（11）
• 页码范围: 2371-2400
• 页数: 30页
• 语种: 英文

摘要

In this paper,we show the Yau's gradient estimate for harmonic maps into a metric space (X,dx) 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 Cheug (1980) and Choi (1982) to harmonic maps into singular spaces.