Abstract
We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. These provide a solution to the long-standing problem of finding a good notion of Ricci flow through singularities, in the $3$-dimensional case.
We prove that Ricci flow with surgery, starting from a fixed initial condition, subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.
Funding Statement
Research supported by NSF grants DMS-1105656, DMS-1207654 and DMS-1405899, and a Simons Fellowship.
Citation
Bruce Kleiner. John Lott. "Singular Ricci flows I." Acta Math. 219 (1) 65 - 134, September 2017. https://doi.org/10.4310/ACTA.2017.v219.n1.a4
