Interpolations, convexity and geometric inequalities
Dario Cordero-Erausquin, Bo'az Klartag
TL;DR
This paper surveys the connections between spectral estimates, degenerate Monge-Ampère equations, and geometric inequalities like Brunn-Minkowski, Santaló, and Busemann, highlighting their interrelated roles in convex geometry and analysis.
Contribution
It provides a comprehensive overview of how spectral estimates and Monge-Ampère equations relate to fundamental geometric inequalities.
Findings
Identifies links between spectral estimates and geometric inequalities.
Explores the role of Monge-Ampère equations in convex geometric analysis.
Highlights the interplay between analysis and geometry in inequality proofs.
Abstract
We survey some interplays between spectral estimates of H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o or Busemann inequalities.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities