Lipschitz continuity of harmonic maps between Alexandrov spaces

2013/11/06 by Zhang, Hui-Chun, Zhu, Xi-Ping · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1311.1331

Abstract

In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally Hölder continuous. In [39], F. H. Lin proposed a challenge problem: Can the Hölder continuity be improved to Lipschitz continuity? J. Jost also asked a similar problem about Lipschitz regularity of harmonic maps between singular spaces (see Page 38 in [28]). The main theorem of this paper gives a complete resolution to it.

Cited by

• Regularity for quasilinear elliptic equations in metric measure spaces
• Lipschitz continuity of harmonic maps between \rm RCD(K,N) spaces and \rm CAT(κ) spaces

Related

• Partial regularity of harmonic maps from Alexandrov spaces
• Lipschitz continuity of harmonic maps between \rm RCD(K,N) spaces and \rm CAT(κ) spaces
• Lipschitz regularity of sub-elliptic harmonic maps into CAT(0) spaces
• Hölder continuity of Minimizing W^s,p-Harmonic Maps
• Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces