5 papers
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}\…
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…
Compactness of the dual Minkowski problem in
Karoly J. Boroczky, Shibing Chen, Weiru Liu +1
We prove the estimate for the th dual Minkowski problem on under fairly general conditions; namely, when lies in [0,1) and , and the th dua…
Uniqueness in the near isotropic Lp dual Minkowski problem
Karoly J. Boroczky, Shibing Chen, Weiru Liu +1
For n>1 and -1<p<1, we prove that if q is close to n and the qth Lp dual curvature is Holder close to be the constant one function, then this "near isotropic" qth Lp dual Minkowski…
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.…