The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the
area of suitable surfaces that represent black holes. Its validity is supported by the cosmic …

We consider surfaces with constant mean curvature in certain warped product manifolds. We
show that any such surface is umbilic, provided that the warping factor satisfies certain …

Geometrical inequalities show how certain parameters of a physical system set restrictions
on other parameters. For instance, a black hole of given mass can not rotate too fast, or an …

The question of isoperimetry What is the largest amount of volume that can be enclosed by a
given amount of area? can be traced back to antiquity. 1 The first mathematically rigorous …

Let (M, g) be an asymptotically flat Riemannian 3‐manifold with nonnegative scalar
curvature and positive mass. We show that each leaf of the canonical foliation of the end of …

Isoperimetric problems for spacelike domains in generalized Robertson–Walker spaces |
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We prove existence of isoperimetric regions for every volume in non-compact Riemannian $
n $-manifolds $(M, g) $, $ n\geq 2$, having Ricci curvature $ Ric_g\geq (n-1) k_0 g $ and …

We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds
with nonnegative scalar curvature and connected horizon boundary, provided the optimal …

We show the existence of isoperimetric regions of sufficiently large volumes in general
asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate …

We survey some results on scalar curvature and properties of solutions to the Einstein
constraint equations. Topics include an extended discussion of asymptotically flat solutions …