One more proof of the Alexandrov-Fenchel inequality
D. Cordero-Erausquin, B. Klartag, Q. Merigot, F. Santambrogio
TL;DR
This paper provides a concise proof of the Alexandrov-Fenchel inequalities, which are fundamental results in convex geometry relating mixed volumes of convex bodies.
Contribution
The authors introduce a new, shorter proof of the Alexandrov-Fenchel inequalities, simplifying previous approaches in convex geometry.
Findings
Confirmed the validity of the inequalities with a more straightforward proof
Enhanced understanding of mixed volume relationships
Potentially simplified future proofs in convex geometry
Abstract
We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Diffusion and Search Dynamics