On Type-I singularities in Ricci flow
- We define several notions of singular set for Type-I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber [15]. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type-I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow [22].
| Author details: | Jörg Enders, Reto Müller, Peter M. Topping |
|---|---|
| ISSN: | 1019-8385 |
| Title of parent work (English): | Communications in analysis and geometry |
| Publisher: | International Press of Boston |
| Place of publishing: | Somerville |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2011 |
| Publication year: | 2011 |
| Release date: | 2017/03/26 |
| Volume: | 19 |
| Issue: | 5 |
| Number of pages: | 18 |
| First page: | 905 |
| Last Page: | 922 |
| Funding institution: | Leverhulme Trust; FIRB |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
