Ancient solutions to the Ricci flow in dimension $3$

By S. Brendle. Acta Mathematica, 2018

78 citations recorded by the source corpus.

It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\kappa$-solution. We prove that the every noncompact ancient $\kappa$-solution in dimension $3$ is isometric to either the shrinking cylinders (or a quotient thereof), or the Bryant soliton.

Subfields: Applied Mathematics, Geometry and Topology, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/15ce848dee90fae910146739c105851e254f6edf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Robert Haslhofer
2. Or Hershkovits
3. Kyeongsu Choi
4. B. White
5. Bruce Kleiner
6. G. Huisken
7. S. Brendle
8. Carlo Sinestrari

In Geometry and Topology

1. Robert Haslhofer
2. Kyeongsu Choi
3. Or Hershkovits
4. B. White
5. Bruce Kleiner
6. S. Brendle
7. G. Huisken
8. A. Neves

In Radiology, Nuclear Medicine and Imaging

1. Robert Haslhofer
2. Or Hershkovits
3. Kyeongsu Choi
4. B. White

Citations in the corpus

• Ancient asymptotically cylindrical flows and applications (2019, result): “We also note that Bamler-Kleiner [BK21] later found an alternative proof of rotational symmetry in the compact case, which uses results and ideas from [Bre20].”