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Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition
Joel Fine, Kirill Krasnov, Michael Singer
Let (M,g) be a compact oriented Einstein 4-manifold. Write R-plus for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if R-plus is negative d…
A gauge theoretic approach to Einstein 4-manifolds
Joel Fine, Kirill Krasnov, Dmitri Panov
This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the math…
Some open questions on anti-de Sitter geometry
Thierry Barbot, Francesco Bonsante, Jeffrey Danciger +6
We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with…
The Weil-Petersson metric and the renormalized volume of hyperbolic 3-manifolds
Kirill Krasnov, Jean-Marc Schlenker
We survey the renormalized volume of hyperbolic 3-manifolds, as a tool for Teichmuller theory, using simple differential geometry arguments to recover results sometimes first achie…
A symplectic map between hyperbolic and complex Teichmüller theory
Kirill Krasnov, Jean-Marc Schlenker
Let be a closed, orientable surface of genus at least 2. The cotangent bundle of the "hyperbolic'' Teichmüller space of can be identified with the space $\CP$ of complex pr…
On the renormalized volume of hyperbolic 3-manifolds
Kirill Krasnov, Jean-Marc Schlenker
The renormalized volume of hyperbolic manifolds is a quantity motivated by the AdS/CFT correspondence of string theory and computed via a certain regularization procedure. The main…
Minimal surfaces and particles in 3-manifolds
Kirill Krasnov, Jean-Marc Schlenker
We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliatio…