A Schwarz lemma of harmonic maps into metric spaces
We established a Schwarz lemma for harmonic maps from Riemannian manifolds to metric spaces of curvature bounded above in the sense of Alexandrov. We adopted the gradient estimate technique which was based on Zhang-Zhu's maximum principle. In particular, when the domain manifold was a hyperboli...
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024276 |
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| author | Jie Wang |
| author_facet | Jie Wang |
| author_sort | Jie Wang |
| collection | DOAJ |
| description | We established a Schwarz lemma for harmonic maps from Riemannian manifolds to metric spaces of curvature bounded above in the sense of Alexandrov. We adopted the gradient estimate technique which was based on Zhang-Zhu's maximum principle. In particular, when the domain manifold was a hyperbolic surface, the energy of any conformal harmonic maps into $ \operatorname{CAT}(-1) $ spaces were bounded from above uniformly. |
| format | Article |
| id | doaj-art-cdcb3f1900004df78b80ba4ddd3fb246 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-cdcb3f1900004df78b80ba4ddd3fb2462025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132115966597410.3934/era.2024276A Schwarz lemma of harmonic maps into metric spacesJie Wang0School of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaWe established a Schwarz lemma for harmonic maps from Riemannian manifolds to metric spaces of curvature bounded above in the sense of Alexandrov. We adopted the gradient estimate technique which was based on Zhang-Zhu's maximum principle. In particular, when the domain manifold was a hyperbolic surface, the energy of any conformal harmonic maps into $ \operatorname{CAT}(-1) $ spaces were bounded from above uniformly.https://www.aimspress.com/article/doi/10.3934/era.2024276harmonic mapssingular spacesschwarz lemmamaximum principlealexandrov curveture bound |
| spellingShingle | Jie Wang A Schwarz lemma of harmonic maps into metric spaces Electronic Research Archive harmonic maps singular spaces schwarz lemma maximum principle alexandrov curveture bound |
| title | A Schwarz lemma of harmonic maps into metric spaces |
| title_full | A Schwarz lemma of harmonic maps into metric spaces |
| title_fullStr | A Schwarz lemma of harmonic maps into metric spaces |
| title_full_unstemmed | A Schwarz lemma of harmonic maps into metric spaces |
| title_short | A Schwarz lemma of harmonic maps into metric spaces |
| title_sort | schwarz lemma of harmonic maps into metric spaces |
| topic | harmonic maps singular spaces schwarz lemma maximum principle alexandrov curveture bound |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024276 |
| work_keys_str_mv | AT jiewang aschwarzlemmaofharmonicmapsintometricspaces AT jiewang schwarzlemmaofharmonicmapsintometricspaces |