Foliation of an Asymptotically Flat End by Critical Capacitors
Please always quote using this URN: urn:nbn:de:bvb:20-opus-269997
- 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 nonlocal nature of our problem.
Author: | Mouhammed Moustapha Fall, Ignace Aristide Minlend, Jesse Ratzkin |
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URN: | urn:nbn:de:bvb:20-opus-269997 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | The Journal of Geometric Analysis |
ISSN: | 1559-002X |
Year of Completion: | 2022 |
Volume: | 32 |
Issue: | 2 |
Article Number: | 54 |
Source: | The Journal of Geometric Analysis 2022, 32(2):54. DOI: 10.1007/s12220-021-00746-6 |
DOI: | https://doi.org/10.1007/s12220-021-00746-6 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | asymptotically flat ends; foliation; over-determined problem |
Release Date: | 2022/06/15 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |