A Liouville-type theorem for Finslerian exponentially harmonic functions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910867809894400 |
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| author | Shen, Bin |
| author_facet | Shen, Bin |
| contents | In this manuscript, we investigate the exponentially harmonic equation on noncompact forward complete Finsler metric measure spaces. We demonstrate that this Finslerian equation represents a critical point of an exponential energy functional. Furthermore, we establish that any bounded solution to this equation is constant, provided that the mixed weighted Ricci curvature is nonnegative and certain additional non-Riemannian tensors are bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Liouville-type theorem for Finslerian exponentially harmonic functions Shen, Bin Differential Geometry In this manuscript, we investigate the exponentially harmonic equation on noncompact forward complete Finsler metric measure spaces. We demonstrate that this Finslerian equation represents a critical point of an exponential energy functional. Furthermore, we establish that any bounded solution to this equation is constant, provided that the mixed weighted Ricci curvature is nonnegative and certain additional non-Riemannian tensors are bounded. |
| title | A Liouville-type theorem for Finslerian exponentially harmonic functions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.07623 |