TY - JOUR

T1 - On a localized Riemannian Penrose inequality

AU - Miao, Pengzi

PY - 2009

Y1 - 2009

N2 - Let Omega be a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary partial derivative Omega is the disjoint union of two pieces: Sigma(H) and Sigma(O), where Sigma(H) consists of the unique closed minimal surfaces in Omega and Sigma(O) is metrically a round sphere. We obtain an inequality relating the area of Sigma(H) to the area and the total mean curvature of Sigma(O). Such an Omega may be thought of as a region, surrounding the outermost apparent horizons of black holes, in a time-symmetric slice of a space-time in the context of general relativity. The inequality we establish has close ties with the Riemannian Penrose Inequality, proved by Huisken and Ilmanen [9] and by Bray [5].

AB - Let Omega be a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary partial derivative Omega is the disjoint union of two pieces: Sigma(H) and Sigma(O), where Sigma(H) consists of the unique closed minimal surfaces in Omega and Sigma(O) is metrically a round sphere. We obtain an inequality relating the area of Sigma(H) to the area and the total mean curvature of Sigma(O). Such an Omega may be thought of as a region, surrounding the outermost apparent horizons of black holes, in a time-symmetric slice of a space-time in the context of general relativity. The inequality we establish has close ties with the Riemannian Penrose Inequality, proved by Huisken and Ilmanen [9] and by Bray [5].

UR - http://apps.isiknowledge.com.ezproxy.lib.monash.edu.au/full_record.do?product=UA&search_mode=GeneralSearch&qid=2&SID=Y2nbAm2CIG4g@dc25dC&page=1&doc=1&

M3 - Article

SN - 0010-3616

VL - 292

SP - 271

EP - 284

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -