Uniqueness of two-convex closed ancient solutions to the mean curvature flow

By Sigurd B. Angenent, P. Daskalopoulos, N. Šešum. Annals of Mathematics, 2018

104 citations recorded by the source corpus.

In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow ($n \ge 2$) which are uniformly two-convex. We prove that any two such ancient solutions are the same up to translations and scaling. In particular, they must coincide up to translations and scaling with the rotationally symmetric closed ancient non-collapsed solution constructed by Brian White in (2000), and by Robert Haslhofer and Or Hershkovits in (2016).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/06263b2ef7adf15e9a7bb61bd545102a59faf196

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

Citations in the corpus

• Ancient asymptotically cylindrical flows and applications (2019, background): “Therefore, by Angenent-DaskalopoulosSesum [ADS20], we conclude thatM is an ancient oval.”