Stability of Ricci de Turck flow on Singular Spaces

TL;DR

This paper proves the stability of Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities, showing convergence under specific stability and integrability conditions.

Contribution

It establishes the stability and convergence of Ricci de Turck flow on singular spaces with conical singularities, extending previous smooth results.

Findings

Flow converges to Ricci-flat metrics with conical singularities

Characterization of stable conical singularities

Examples satisfying integrability condition

Abstract

In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we construct a Ricci de Turck flow which starts sufficiently close to a Ricci-flat metric with isolated conical singularities and converges to a singular Ricci-flat metric under an assumption of integrability, linear and tangential stability. We provide a characterization of conical singularities satisfying tangential stability and discuss examples where the integrability condition is satisfied.