Singular Yamabe Problem Willmore Energies
Differential Geometry
2015-08-11 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Abstract
We develop the calculus for hypersurface variations based on variation of the hypersurface defining function. This is used to show that the functional gradient of a new Willmore-like, conformal hypersurface energy agrees exactly with the obstruction to smoothly solving the singular Yamabe problem for conformally compact four-manifolds. We give explicit hypersurface formulae for both the energy functional and the obstruction.
Keywords
Cite
@article{arxiv.1508.01838,
title = {Singular Yamabe Problem Willmore Energies},
author = {Michael Glaros and A. Rod Gover and Matthew Halbasch and Andrew Waldron},
journal= {arXiv preprint arXiv:1508.01838},
year = {2015}
}
Comments
36 pages, LaTeX