An r-hyperconvex body is a set in the d-dimensional Euclidean space Ed that is the intersection of a family of closed balls of radius r. We prove the analogue of the classical Blaschke-Santallo inequality for r-hyperconvex bodies, and we also establish a stability version of it. The other main result of the paper is an r-hyperconvex version of the reverse isoperimetric inequality in the plane
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bod...
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Eu...
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show h...
A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of cl...
We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic sp...
A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of cl...
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction...
We strengthen the volume inequalities for L-p zonoids of even isotropic measures and for their duals...
AbstractAn important GL(n) invariant functional of centred (origin symmetric) convex bodies that has...
Abstract. We prove that the area of a hypersurface Σ which traps a given volume outside a convex dom...
Abstract. For a convex body of given volume in spherical space, the total invariant measure of hitti...
Abstract from public.pdf file.Dissertation supervisor: Dr. Alexander Koldobsky.Includes vita.This th...
For every hyperplane $H$ supporting a convex body $C$ in the hyperbolic space $\mathbb{H}^d$ we defi...
We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inrad...
AbstractWe introduce a method which leads to upper bounds for the isotropic constant. We prove that ...
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bod...
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Eu...
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show h...
A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of cl...
We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic sp...
A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of cl...
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction...
We strengthen the volume inequalities for L-p zonoids of even isotropic measures and for their duals...
AbstractAn important GL(n) invariant functional of centred (origin symmetric) convex bodies that has...
Abstract. We prove that the area of a hypersurface Σ which traps a given volume outside a convex dom...
Abstract. For a convex body of given volume in spherical space, the total invariant measure of hitti...
Abstract from public.pdf file.Dissertation supervisor: Dr. Alexander Koldobsky.Includes vita.This th...
For every hyperplane $H$ supporting a convex body $C$ in the hyperbolic space $\mathbb{H}^d$ we defi...
We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inrad...
AbstractWe introduce a method which leads to upper bounds for the isotropic constant. We prove that ...
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bod...
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Eu...
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show h...
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