A mass-decreasing flow in dimension three

TL;DR

This paper introduces a novel mass-decreasing flow for asymptotically flat three-manifolds, combining Ricci flow with surgery and conformal rescaling, leading to mass reduction and topological simplification.

Contribution

It presents a new flow that decreases mass in three-manifolds and analyzes its properties, including topological changes and a monotone energy functional.

Findings

Wormholes pinch off in finite time

Nontrivial spherical space forms bubble off

Flow reduces initial mass under certain conditions

Abstract

In this article, we introduce a mass-decreasing flow for asymptotically flat three-manifolds with nonnegative scalar curvature. This flow is defined by iterating a suitable Ricci flow with surgery and conformal rescalings and has a number of nice properties. In particular, wormholes pinch off and nontrivial spherical space forms bubble off in finite time. Moreover, a noncompact variant of the Perelman-energy is monotone along the flow. Assuming a certain inequality between the mass and this Perelman-energy a priori, we can prove that the flow squeezes out all the initial mass.