Exponentially harmonic maps of complete Riemannian manifolds


We note the existence of exponentially harmonic maps from complete Riemannian manifolds into arbitrary compact Riemannian manifolds. We also investigate the constancy of exponentially harmonic maps with finite exponential energy under some curvature assumptions.

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The author would like to thank the referee for her or his careful reading of the manuscript and many helpful suggestions. he is partially supported by Grant-in-Aid for Young Scientists (B) (KAKENHI No. 15K17546) and also by Grant-in-Aid for Scientific Research on Innovative Areas (KAKENHI No. 17H06466) both from JSPS. This work is also supported by JST CREST Grant Number JPMJCR17J4.

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Correspondence to Toshiaki Omori.

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Omori, T. Exponentially harmonic maps of complete Riemannian manifolds. manuscripta math. 161, 205–212 (2020). https://doi.org/10.1007/s00229-018-1084-2

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Mathematics Subject Classification

  • Primary 53C43
  • 58E20