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キーワード:
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要旨:
LetM 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.
