73 citations · 282 across the 34 of their papers we have counts for
5 papers · 1 filter
Remarks on planar Blaschke-Santaló inequality
K. J. Böröczky, E. Makai
We prove the Blaschke-Santaló inequality restricted to -gons: the extremal polygons are the affine regular -gons. If either the John or the Löwner ellipse of a planar -sym…
Isotropic measures, and stronger forms of the reverse isoperimetric inequality
Karoly J. Boroczky, Daniel Hug
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
The cone volume measure of antipodal points
Karoly J. Böröczky, Pal Hegedus
The optimal condition of the cone volume measure of a pair of antopodal points is proved and analyzed.
The discrete logarithmic Minkowski problem
Karoly J. Boroczky, Pal Hegedus, Guangxian Zhu
Existence of solution of the logarithmic Minkowski problem is proved for the case where the discrete measures on the unit sphere satisfy the subspace concentration condition with r…
Cone-volume measure and stability
Károly J. Böröczky, Martin Henk
We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This implies, among others, a conjectured best pos…