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

Brendle, Simon¹ ; Naff, Keaton²

¹ Department of Mathematics, Columbia University, New York, NY, United States
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 27 (2023) no. 1, pp. 153-226.

Résumé

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

Détail

DOI : 10.2140/gt.2023.27.153

Keywords: Ricci flow, rotational symmetry, ancient solutions, higher dimensions

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