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math.MG2020★ 1 cited
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…
math.MG2019★ 17 cited
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…
math.MG2018★ 23 cited
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…