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math.MG2026
On Ball's conjectured Santaló type inequality
Károly J. Böröczky, Konstantinos Patsalos, Christos Saroglou
We prove that if is a symmetric and isotropic convex body in , then $$\int_K\langle x,u\rangle^2\,dx\int_{K^\circ}\langle x,u\rangle^2\,dx\leq \left(\int_{B_2^n}\…
math.MG2024
A note on the -Brunn-Minkowski inequality for intrinsic volumes and the -Christoffel-Minkowski problem
Konstantinos Patsalos, Christos Saroglou
The first goal of this paper is to improve some of the results in \cite{BCPR}. Namely, we establish the -Brunn-Minkwoski inequality for intrinsic volumes for origin-symmetric…
math.MG2024
Complex and Quaternionic Analogues of Busemann's Random Simplex and Intersection Inequalities
Christos Saroglou, Thomas Wannerer
In this paper, we extend two celebrated inequalities by Busemann -- the random simplex inequality and the intersection inequality -- to both complex and quaternionic vector spaces.…