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arXiv · 2610.08746

Hyperbolicity Beyond Convexity in the Alexandrov-Fenchel Inequality

Leo Brauner·Oscar Ortega-Moreno
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Abstract

We establish an Alexandrov--Fenchel type inequality in which one of the reference bodies is replaced by a function whose Hessian satisfies a balancing condition on its eigenvalues, without being required to be positive semidefinite. The proof hinges on a new extension of Alexandrov's inequality for mixed discriminants. As applications, we derive a log-concavity principle for linear functionals of area measures, answering a question of Colesanti, Hug, and Saorín-Gómez, as well as Brunn--Minkowski type inequalities for intrinsic volumes of mean section bodies, answering a question of Schuster.

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Leo Brauner, Oscar Ortega-Moreno. 2026-10-06. Hyperbolicity Beyond Convexity in the Alexandrov-Fenchel Inequality. https://arxiv.org/abs/2610.08746

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