Curvature bounds by isoperimetric comparison for normalized Ricci flow on the two-sphere
We prove a comparison theorem for the isoperimetric profiles of solutions of the normalized Ricci flow on the two-sphere: If the isoperimetric profile of the initial metric is greater than that of some positively curved axisymmetric metric, then the inequality remains true for the isoperimetric profiles of the evolved metrics. We apply this using the Rosenau solution as the model metric to deduce sharp time-dependent curvature bounds for arbitrary solutions of the normalized Ricci flow on the...[Show more]
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|Source:||Calculus of Variations and Partial Differential Equations - Online|
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