Prescribing curvatures on surfaces with conical singularities and corners
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916899775840256 |
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| author | Battaglia, Luca Reyes-Sanchez, Francisco Javier |
| author_facet | Battaglia, Luca Reyes-Sanchez, Francisco Javier |
| contents | This paper is concerned with the problem of prescribing Gaussian curvature and geodesic curvature in a compact surface with boundary with conical singularities and corners. Solutions are obtained using a new variational formulation, recently introduced for the regular counterpart of the problem and extended here to the singular case. As far as we know, this is the first result for the problem of prescribed curvatures in surfaces with singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prescribing curvatures on surfaces with conical singularities and corners Battaglia, Luca Reyes-Sanchez, Francisco Javier Analysis of PDEs Differential Geometry 35J20, 58J32, 53A30, 35B44 This paper is concerned with the problem of prescribing Gaussian curvature and geodesic curvature in a compact surface with boundary with conical singularities and corners. Solutions are obtained using a new variational formulation, recently introduced for the regular counterpart of the problem and extended here to the singular case. As far as we know, this is the first result for the problem of prescribed curvatures in surfaces with singularities. |
| title | Prescribing curvatures on surfaces with conical singularities and corners |
| topic | Analysis of PDEs Differential Geometry 35J20, 58J32, 53A30, 35B44 |
| url | https://arxiv.org/abs/2502.15976 |