Prescribing nearly constant curvatures on balls
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915334021185536 |
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| author | Battaglia, Luca Cruz-Blázquez, Sergio Pistoia, Angela |
| author_facet | Battaglia, Luca Cruz-Blázquez, Sergio Pistoia, Angela |
| contents | In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R^2, and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov-Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09622 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Prescribing nearly constant curvatures on balls Battaglia, Luca Cruz-Blázquez, Sergio Pistoia, Angela Analysis of PDEs Differential Geometry 35J25, 58J32 In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R^2, and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov-Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants. |
| title | Prescribing nearly constant curvatures on balls |
| topic | Analysis of PDEs Differential Geometry 35J25, 58J32 |
| url | https://arxiv.org/abs/2305.09622 |