Continuity of Ricci Flow Through Neck Pinch Singularities

Abstract

In this article, we consider the Angenent-Caputo-Knopf's Ricci Flow through neckpinch singularities. We will explain how one can see the A-C-K's Ricci flow through a neckpinch singularity as a flow of integral current spaces. We then prove the continuity of this weak flow with respect to the Sormani-Wenger Intrinsic Flat (SWIF) distance.

21 pages, 4 figures

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by in corpus (2)

• Properties of the Intrinsic Flat Distance
• Diameter Controls and Smooth Convergence away from Singular Sets