1 citations · 1 across the 9 of their papers we have counts for
14 papers
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…
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,…
Aomoto interpolation and Coxeter systems
Ángel D. Martínez, Oscar Ortega-Moreno
In this paper, we construct a Lagrange-type basis for the Aomoto space , naturally indexed by the chambers of the hyperplane arrangement . The construct…
Polarization problems and Coxeter systems
Ángel D. Martínez, Oscar Ortega-Moreno
In this paper we provide a proof of the strong polarization conjecture due to Ball and Frenkel. We observe that Coxeter systems produce unexpected new examples of extremizers. Furt…
Strong Polarization and Entropy
Daniel Galicer, Oscar Ortega-Moreno, Damián Pinasco
We show that for any set of unit vectors in a real Hilbert space and positive numbers satisfying , there exists a unit vector…
Mixed Christoffel-Minkowski problems for bodies of revolution
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
The mixed Christoffel-Minkowski problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bo…
The Christoffel problem for the disk area measure
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
The mixed Christoffel problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bodies, all…
The Klain approach to zonal valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We show an analogue of the Klain-Schneider theorem for valuations that are invariant under rotations around a fixed axis, called zonal. Using this, we establish a new integral repr…
Lefschetz operators on convex valuations
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
We investigate the action of Alesker's Lefschetz operators on translation invariant valuations on convex bodies. For scalar valued valuations, we describe this action on the level…
Fixed Points of Mean Section Operators
Leo Brauner, Oscar Ortega-Moreno
We characterize rotation equivariant bounded linear operators from to by the mass distribution of the spherical Laplacian of their ker…
Iterations of Minkowski Valuations
Oscar Ortega-Moreno
It is shown that for any sufficiently regular even Minkowski valuation which is homogeneous and intertwines rigid motions, and for any convex body in a smooth neighborhood…
The complex plank problem, revisited
Oscar Ortega-Moreno
Ball's complex plank theorem states that if are unit vectors in , and , non-negative numbers satisfying then t…
Fixed points of Minkowski valuations
Oscar Ortega-Moreno, Franz E. Schuster
It is shown that for any sufficiently regular even Minkowski valuation which is homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball, where b…
An Optimal Plank Theorem
Oscar Ortega-Moreno
We give a new proof of Fejes Tóth's zone conjecture: for any sequence of unit vectors in a real Hilbert space , there exists a unit vector in $\m…