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Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions

Simon Brendle and Keaton Naff

Geometry & Topology 27 (2023) 153–226
Abstract

We extend work of the first author on the uniqueness of ancient κ–solutions to higher dimensions. In dimensions n 4, an ancient κ–solution is a nonflat, complete, ancient solution of the Ricci flow that is uniformly PIC and weakly PIC2, has bounded curvature and is κ–noncollapsed. We show that the only noncompact ancient κ–solutions up to isometry are a family of shrinking cylinders, a quotient thereof, or the Bryant soliton.

Keywords
Ricci flow, rotational symmetry, ancient solutions, higher dimensions
Mathematical Subject Classification
Primary: 53E20
References
Publication
Received: 28 November 2020
Accepted: 16 September 2021
Published: 1 May 2023
Proposed: Tobias H Colding
Seconded: John Lott, Bruce Kleiner
Authors
Simon Brendle
Department of Mathematics
Columbia University
New York, NY
United States
Keaton Naff
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States

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