Department of Mathematics
Singular Yamabe Problem Willmore Energies
- Author(s): Glaros, Michael
- Gover, A. Rod
- Halbasch, Matthew
- Waldron, Andrew
- et al.
Published Web Locationhttps://arxiv.org/pdf/1508.01838.pdf
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.