2015/08/07 by Michael Glaros, Glaros, Michael, A. Rod Gover +5
Mathematics · Physics and Astronomy · #53A30 (primary) #53A55 #53B15 #58E30 #83C99 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #gr-qc #hep-th #math.DG #msc:53A30 #msc:53A55 #msc:53B15 #msc:58E30 #msc:83C99
paper · pdf · doi:10.48550/arxiv.1508.01838
36 pages, LaTeX
arxiv created 2015/08/07 · arxiv updated 2015/08/11
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.