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Harmonic Maps Between Alexandrov Spaces

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Abstract

In this paper, we shall discuss the existence, uniqueness and regularity of harmonic maps from an Alexandrov space into a geodesic space with curvature \(\leqslant 1\) in the sense of Alexandrov.

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Notes

  1. In [5, 14, 27], Sobolev spaces are defined on metric measure spaces supporting a doubling condition and a Poincaré inequality.

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Acknowledgments

The second author is partially supported by NSFC 11201492.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Jia-Cheng Huang & Hui-Chun Zhang

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  1. Jia-Cheng Huang
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  2. Hui-Chun Zhang
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Correspondence to Jia-Cheng Huang.

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Huang, JC., Zhang, HC. Harmonic Maps Between Alexandrov Spaces. J Geom Anal 27, 1355–1392 (2017). https://doi.org/10.1007/s12220-016-9722-y

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  • DOI: https://doi.org/10.1007/s12220-016-9722-y

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