Foliation of an asymptotically flat end by critical capacitors
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866917952362643456 |
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| author | Fall, Mouhammed Moustapha Minlend, Ignace Aristide Ratzkin, Jesse |
| author_facet | Fall, Mouhammed Moustapha Minlend, Ignace Aristide Ratzkin, Jesse |
| contents | We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace-Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the non-local nature of our problem |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_05323 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Foliation of an asymptotically flat end by critical capacitors Fall, Mouhammed Moustapha Minlend, Ignace Aristide Ratzkin, Jesse Analysis of PDEs Differential Geometry 58J05, 58J32, 58J37, 35N10, 35N25 We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate spheres, and they admit solutions of a certain over-determined boundary value problem involving the Laplace-Beltrami operator. In a key step we must invert the Dirichlet-to-Neumann operator, highlighting the non-local nature of our problem |
| title | Foliation of an asymptotically flat end by critical capacitors |
| topic | Analysis of PDEs Differential Geometry 58J05, 58J32, 58J37, 35N10, 35N25 |
| url | https://arxiv.org/abs/2007.05323 |