Uniqueness of compact ancient solutions to the higher dimensional Ricci\n flow

2021/02/14 by Simon Brendle, Brendle, Simon, Panagiota Daskalopoulos +5 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2102.07180

Abstract

In this paper, we study the classification of \κ-noncollapsed ancient\nsolutions to n-dimensional Ricci flow on Sⁿ, extending the result in [13] to\nhigher dimensions. We prove that such a solution is either isometric to a\nfamily of shrinking round spheres, or the Type II ancient solution constructed\nby Perelman.\n

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• Mean curvature flow through singularities

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