Foliation of an asymptotically flat end by critical capacitors
Analysis of PDEs
2025-03-13 v1 Differential Geometry
Abstract
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
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Cite
@article{arxiv.2007.05323,
title = {Foliation of an asymptotically flat end by critical capacitors},
author = {Mouhammed Moustapha Fall and Ignace Aristide Minlend and Jesse Ratzkin},
journal= {arXiv preprint arXiv:2007.05323},
year = {2025}
}
Comments
25 pages