Minimally invasive surgery for Ricci flow singularities

Abstract

In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on S^(n+1), without performing an intervening surgery. In the restrictive context of rotational symmetry, this construction gives evidence in favor of Perelman's hope for a "canonically defined Ricci flow through singularities".

References in corpus (3)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture
• Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective