Optimal transport and Perelman's reduced volume
John Lott
TL;DR
This paper demonstrates the convexity of an entropy-like function in an optimal transport setting adapted to Ricci flow, providing a new proof for the monotonicity of Perelman's reduced volume.
Contribution
It introduces a novel optimal transport framework tailored to Ricci flow to reprove Perelman's reduced volume monotonicity.
Findings
Convexity of an entropy-like function under Ricci flow-adapted optimal transport
New proof of Perelman's reduced volume monotonicity
Enhanced understanding of Ricci flow through optimal transport methods
Abstract
We show that a certain entropy-like function is convex, under an optimal transport problem that is adapted to Ricci flow. We use this to reprove the monotonicity of Perelman's reduced volume.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Nonlinear Partial Differential Equations