Unique Asymptotics of Compact Ancient Solutions to <scp>Three‐Dimensional</scp> Ricci Flow
Sigurd Angenent, Simon Brendle, Panagiota Daskalopoulos, Nataša Šešum
Abstract
Abstract We consider compact ancient solutions to the three‐dimensional Ricci flow that are κ ‐noncollapsed. We prove that such a solution either is a family of shrinking round spheres or has a unique asymptotic behavior as t → − ∞ , which we describe. This analysis applies in particular to the ancient solution constructed by Perelman. © 2020 Wiley Periodicals LLC.
Topics & Concepts
Ricci flowMathematicsFlow (mathematics)SPHERESPure mathematicsMathematical analysisRicci curvatureGeometryPhysicsAstronomyCurvatureGeometric Analysis and Curvature FlowsGeometry and complex manifoldsNonlinear Partial Differential Equations