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Inventiones mathematicae

, Volume 211, Issue 3, pp 863–934 | Cite as

Lipschitz continuity of harmonic maps between Alexandrov spaces

  • Hui-Chun Zhang
  • Xi-Ping Zhu
Article

Abstract

In 1997, Jost (Calc Var PDE 5:1–19, 1997) and Lin (Collection of papers on geometry, analysis and mathematical physics, World Sci. Publ., River Edge, 1997), 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. Lin (1997) proposed an open 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 Jost (in: Jost, Kendall, Mosco, Röckner, Sturm (eds) New directions in Dirichlet forms, International Press, Boston, 1998)]. The main theorem of this paper gives a complete resolution to it.

Mathematics Subject Classification

58E20 

Notes

Acknowledgements

Both authors are partially supported by NSFC 11521101. The first author is partially supported by NSFC 11571374 and by “National Program for Support of Top-notch Young Professionals”.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsSun Yat-sen UniversityGuangzhouChina

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