References & Citations
Mathematics > Differential Geometry
Title: The Ricci flow and isoperimetric inequalities on surfaces
(Submitted on 12 Apr 2024)
Abstract: We revisit the connection between the Ricci flow and isoperimetric inequalities on surfaces which are diffeomorphic to the $2$-sphere. We prove that the Cheeger isoperimetric constant is non-decreasing under Ricci flow on topological $2$-spheres. A topological $2$-sphere with non-trivial curvature is exhibited which is a counterexample to the hypothesis that the Cheeger constant is a strictly increasing function of the Ricci flow.
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