TY  - JOUR
A1  - Fall, Mouhammed Moustapha
A1  - Minlend, Ignace Aristide
A1  - Ratzkin, Jesse
T1  - Foliation of an Asymptotically Flat End by Critical Capacitors
JF  - The Journal of Geometric Analysis
N2  - 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.
KW  - asymptotically flat ends
KW  - foliation
KW  - over-determined problem
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-269997
SN  - 1559-002X
VL  - 32
IS  - 2
ER  -