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Uniqueness of Smooth Stationary Black Holes in Vacuum: Small Perturbations of the Kerr Spaces
The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions, a result which we believe will be useful in the proof of their nonlinear stability. Following theExpand
Hawking’s Local Rigidity Theorem Without Analyticity
We prove the existence of a Hawking Killing vector-field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth vacuum Einstein manifold. The result extendsExpand
The decomposition of Global Conformal Invariants V
This is the fifth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be conformallyExpand
On conformally invariant differential operators in odd dimensions
  • S. Alexakis
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences…
  • 1 April 2003
This is a brief announcement in which we identify all the conformally invariant differential operators acting on densities other than −(n/2) + k and other than l, where k is a positive integer and lExpand
Unique continuation for the vacuum Einstein equations
We derive a unique continuation theorem for the vacuum Einstein equations. Our method of proof utilizes Carleman estimates (most importantly one obtained recently by Ionescu and Klainerman), but alsoExpand
The Penrose inequality on perturbations of the Schwarzschild exterior
We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\underline{\mathcal{N}}_0$.Expand
Determining a Riemannian Metric from Minimal Areas
We prove that if $(M,g)$ is a topological 3-ball with a $C^4$-smooth Riemannian metric $g$, and mean-convex boundary $\partial M$, then knowledge of least areas circumscribed by simple closed curvesExpand
Non-existence of time-periodic vacuum spacetimes
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result appliesExpand
On the decomposition of global conformal invariants, I
This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics. The objects of study are scalar RiemannianExpand
On the decomposition of global conformal invariants II
Abstract This paper is a continuation of [S. Alexakis, The decomposition of global conformal invariants I, submitted for publication, see also math.DG/0509571 ], where we complete our partial proofExpand