Variational calculus for hypersurface functionals: Singular Yamabe problem Willmore energies
| Autor: | Andrew Waldron, A. Rod Gover, Michael Glaros, Matthew Halbasch |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
010102 general mathematics
Yamabe problem General Physics and Astronomy Conformal map 01 natural sciences symbols.namesake Willmore energy Hypersurface 0103 physical sciences symbols Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology Calculus of variations 0101 mathematics Einstein Conformal geometry Mathematical Physics Energy functional Mathematics Mathematical physics |
| Zdroj: | Journal of Geometry and Physics. 138:168-193 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/j.geomphys.2018.12.018 |
| Popis: | We develop an efficient calculus for varying hypersurface embeddings based on variations of hypersurface defining functions. 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 formulae for both the energy functional and the obstruction. Vanishing of the latter is a necessary condition for solving the vacuum cosmological Einstein equations in four spacetime dimensions with data prescribed on a conformal infinity, while the energy functional generalizes the scheme-independent contribution to entanglement entropy across surfaces to hypersurfaces. |
| Databáze: | OpenAIRE |
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