211 citations · 985 across the 36 of their papers we have counts for
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The local logarithmic Brunn-Minkowski inequality for zonoids
Ramon van Handel
The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld…
Shephard's inequalities, Hodge-Riemann relations, and a conjecture of Fedotov
Ramon van Handel
A well-known family of determinantal inequalities for mixed volumes of convex bodies were derived by Shephard from the Alexandrov-Fenchel inequality. The classic monograph Geometri…
The Extremals of the Alexandrov-Fenchel Inequality for Convex Polytopes
Yair Shenfeld, Ramon van Handel
The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The cha…
The Extremals of Minkowski's Quadratic Inequality
Yair Shenfeld, Ramon van Handel
In a seminal paper "Volumen und Oberfläche" (1903), Minkowski introduced the basic notion of mixed volumes and the corresponding inequalities that lie at the heart of convex geomet…
Mixed volumes and the Bochner method
Yair Shenfeld, Ramon van Handel
At the heart of convex geometry lies the observation that the volume of convex bodies behaves as a polynomial. Many geometric inequalities may be expressed in terms of the coeffici…