A Survey on the Ricci flow on Singular Spaces
Differential Geometry
2021-01-25 v1 Analysis of PDEs
Abstract
In this survey we provide an overview of our recent results concerning Ricci de Turck flow on spaces with isolated conical singularities. The crucial characteristic of the flow is that it preserves the conical singularity. Under certain conditions, Ricci flat metrics with isolated conical singularities are stable and positive scalar curvature is preserved under the flow. We also discuss the relation to Perelman's entropies in the singular setting, and outline open questions and future reseach directions.
Keywords
Cite
@article{arxiv.2101.09135,
title = {A Survey on the Ricci flow on Singular Spaces},
author = {Klaus Kroencke and Boris Vertman},
journal= {arXiv preprint arXiv:2101.09135},
year = {2021}
}
Comments
17 pages, 1 figure. arXiv admin note: text overlap with arXiv:1802.02908, arXiv:1902.02097, arXiv:2002.06586