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Harmonicity of totally geodesic maps into nonpositively curved metric spaces |
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| Authors: | Shin-ichi?Ohta author-information" > author-information__contact u-icon-before" > mailto:sohta@math.kyoto-u" title=" sohta@math.kyoto-u" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | (1) Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan;(2) Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan |
| Abstract: | We prove the harmonicity of totally geodesic maps from a Riemannian manifold to a nonpositively curved metric space in the sense of Alexandrov for both Korevaar-Schoen-type and Cheeger-type energies. This enables us to make many examples of harmonic maps of an unknown type. We also construct an example of totally geodesic map between CAT(0)-spaces which is not harmonic.Mathematics Subject Classification (2000): 53C22, 53C43, 58E20 |
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