The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality

Huisken, Gerhard; Ilmanen, Tom

J. Differential Geom., Tome 57 (2001) no. 2, p. 353-437 / Harvested from Project Euclid

Résumé

Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass m according to the formula |N| ≤ 16πm². We develop a theory of weak solutions of the inverse mean curvature flow, and employ it to prove this inequality for each connected component of N using Geroch's monotonicity formula for the ADM mass. Our method also proves positivity of Bartnik's gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry.

Publié le : 2001-11-14
Classification:

@article{1090349447,
     author = {Huisken, Gerhard and Ilmanen, Tom},
     title = {The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality},
     journal = {J. Differential Geom.},
     volume = {57},
     number = {2},
     year = {2001},
     pages = { 353-437},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1090349447}
}

Huisken, Gerhard; Ilmanen, Tom. The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality. J. Differential Geom., Tome 57 (2001) no. 2, pp.  353-437. http://gdmltest.u-ga.fr/item/1090349447/