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.

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Author: Mouhammed Moustapha Fall, Ignace Aristide Minlend, Jesse Ratzkin
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Parent Title (English):The Journal of Geometric Analysis
Year of Completion:2022
Article Number:54
Source:The Journal of Geometric Analysis 2022, 32(2):54. DOI: 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):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International