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 Lio...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 Cheng(1980) and Choi(1982) to harmonic maps into singular spaces.展开更多
In this paper,we shall prove that any minimizer of Ginzburg-Landau functional from an Alexandrov space with curvature bounded below into a nonpositively curved metric cone must be locally Lipschitz continuous.
基金supported by National Natural Science Foundation of China (Grant No. 11521101)supported by National Natural Science Foundation of China (Grant No. 11571374)+1 种基金National Program for Support of Top-Notch Young Professionalssupported by the Academy of Finland
文摘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 Cheng(1980) and Choi(1982) to harmonic maps into singular spaces.
文摘In this paper,we shall prove that any minimizer of Ginzburg-Landau functional from an Alexandrov space with curvature bounded below into a nonpositively curved metric cone must be locally Lipschitz continuous.
