A note on Ricci flow and optimal transportation
S. Brendle
TL;DR
This paper explores a novel connection between Ricci flow, specifically Perelman's reduced volume monotonicity, and optimal transport theory, potentially offering new insights into geometric analysis.
Contribution
It introduces a new link between Ricci flow's monotonicity formula and optimal transport, bridging two mathematical areas.
Findings
Establishes a connection between Ricci flow and optimal transport.
Provides new perspectives on Perelman's reduced volume.
Suggests potential for further research in geometric analysis.
Abstract
In this note, we describe a new link between Perelman's monotonicity formula for the reduced volume and ideas from optimal transport theory.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Equations and Dynamical Systems