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math.MG2026
Radon Transforms of Projection Functions and Aleksandrov-Fenchel Inequalities
Leo Brauner, Oscar Ortega-Moreno, Franz E. Schuster
The Radon transforms on Grassmannians define two families of geometric operators on convex bodies when applied to their projection functions. On the one hand, these are Minkowski's…
math.MG2026
Hyperbolicity Beyond Convexity in the Alexandrov-Fenchel Inequality
Leo Brauner, Oscar Ortega-Moreno
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,…