Ricci de Turck flow on singular manifolds

TL;DR

This paper establishes short-term existence and regularity of Ricci de Turck flow on manifolds with incomplete edge singularities, and long-term existence near flat metrics, advancing geometric analysis on singular spaces.

Contribution

It proves local and long-term existence of Ricci de Turck flow on incomplete edge manifolds, extending Ricci flow theory to singular spaces with new analytical techniques.

Findings

Short-time existence of Ricci de Turck flow on incomplete edge manifolds.

Regularity properties of evolving metrics with edge singularities.

Conditions for long-time existence near flat incomplete edge metrics.

Abstract

In this paper we prove local existence of a Ricci de Turck flow starting at a space with incomplete edge singularities and flowing for a short time within a class of incomplete edge manifolds. We derive regularity properties for the corresponding family of Riemannian metrics and discuss boundedness of the Ricci curvature along the flow. For Riemannian metrics that are sufficiently close to a flat incomplete edge metric, we prove long time existence of the Ricci de Turck flow. Under certain conditions, our results yield existence of Ricci flow on spaces with incomplete edge singularities. The proof works by a careful analysis of the Lichnerowicz Laplacian and the Ricci de Turck flow equation.