On valuation deviations and their geometry

2025/11/28 by David Cutler, Cutler, David Owen Horace, Mel Deaton +1
Mathematics · #Point processes and geometric inequalities #Holomorphic and Operator Theory #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2511.23468

Abstract

We introduce two valuation-based deviations on convex bodies. Using a construction that allows us to associate to these deviations "intrinsic" pseudometrics, we establish various results which capture information about the underlying valuation in terms of the geometry of their induced deviations.

Citations

• On Minkowski's monotonicity problem
• The Hausdorff distance and metrics on toric singularity types
• The support of mixed area measures involving a new class of convex bodies
• A unified treatment for Lp Brunn-Minkowski type inequalities

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