Infinitely many solutions for a boundary Yamabe problem
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909661170499584 |
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| author | Battaglia, Luca Vaira, Giusi Pu, Yixing |
| author_facet | Battaglia, Luca Vaira, Giusi Pu, Yixing |
| contents | We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature in the unit ball endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence of infinitely many non-radial positive solutions when the dimension is larger or equal to 5. This is the first result of existence of solutions in the case of negative prescribed scalar curvature problem in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions for a boundary Yamabe problem Battaglia, Luca Vaira, Giusi Pu, Yixing Analysis of PDEs Differential Geometry We consider the classical geometric problem of prescribing the scalar and the boundary mean curvature in the unit ball endowed with the standard Euclidean metric. We will deal with the case of negative scalar curvature showing the existence of infinitely many non-radial positive solutions when the dimension is larger or equal to 5. This is the first result of existence of solutions in the case of negative prescribed scalar curvature problem in higher dimensions. |
| title | Infinitely many solutions for a boundary Yamabe problem |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2503.06192 |