Lower semicontinuity of mass under $C^0$ convergence and Huisken's isoperimetric mass

Autor:	Jauregui, Jeffrey L., Lee, Dan A.
Rok vydání:	2016
Předmět:	Mathematics - Differential Geometry General Relativity and Quantum Cosmology 53C20 (Primary) 83C99 58Z05 (Secondary)
Zdroj:	Journal fuer die reine und angewandte Mathematik (Crelle's Journal), Vol. 2019, No. 756, pg. 227-257
Druh dokumentu:	Working Paper
Popis:	Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed $C^0$ Cheeger--Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. In other words, total mass is lower semicontinuous under such convergence. In order to prove this, we use Huisken's isoperimetric mass concept, together with a modified weak mean curvature flow argument. We include a brief discussion of Huisken's work before explaining our extension of that work. The results are all specific to three dimensions. Comment: 30 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.00732 Zobrazit plný text záznamu View this record from Arxiv