73 citations · 282 across the 34 of their papers we have counts for
23 papers · 1 filter
Approximate isoperimetry for convex polytopes
Keith Ball, Károly J. Böröczky, Assaf Naor
For all with , the smallest possible isoperimetric quotient of an -dimensional convex polytope that has facets is shown to be bounded fro…
Hyperbolic width functions and characterizations of bodies of constant width in the hyperbolic space
Károly J. Böröczky, András Csépai, Ádám Sagmeister
We discuss basic properties of several different width functions in the -dimensional hyperbolic space such as continuity, and we also define a new hyperbolic width as the extens…
A quantitative stability result for the sphere packing problem in dimensions 8 and 24
Károly J. Böröczky, Danylo Radchenko, João P. G. Ramos
We prove explicit stability estimates for the sphere packing problem in dimensions 8 and 24, showing that, in the lattice case, if a lattice is close to satisfyi…
Stability of the isodiametric problem on the sphere and in the hyperbolic space
Károly J. Böröczky, Ádám Sagmeister
We prove a stability version of the isodiametric inequality on the sphere and in the hyperbolic space.
Stability of the log-Brunn-Minkowski inequality in the case of many hyperplane symmetries
Karoly Boroczky, Apratim De
In the case of symmetries with respect to n independent linear hyperplanes, a stability version of the logarithmic Brunn-Minkowski inequality and the logarithmic Minkowski inequali…
Strengthened inequalities for the mean width and the -norm
Károly J. Böröczky, Ferenc Fodor, Daniel Hug
Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; o…
-equivariant and translation covariant continuous tensor valuations
Judit Abardia-Evéquoz, Károly J. Böröczky, Mátyás Domokos +1
The space of continuous, -equivariant, , and translation covariant valuations taking values in the space of real symmetric tensors on of r…
Smoothness in the Minkowski problem for
Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti
We discuss the smoothness and strict convexity of the solution of the Minkowski problem when and the given measure has a positive density function.
Minkowski valuations on lattice polytopes
Karoly J. Boroczky, Monika Ludwig
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In t…
Volume product of planar polar convex bodies --- lower estimates with stability
K. J. Böröczky, E. Makai, M. Meyer +1
Let be an -symmetric convex body, and its polar body. Then we have , with equality if and only if is a parallelogram. (…
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…
Stability of the functional forms of the Blaschke-Santalo inequality
Franck Barthe, Karoly J. Boroczky, Matthieu Fradelizi
Stability versions of the functional forms of the Blaschke-Santalo inequality due to Ball, Artstein-Klartag-Milman, Fradelizi-Meyer and Lehec are proved.
Remarks on the equality case of the Bonnesen inequality
Karoly J. Boroczky, Oriol Serra
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presen…
Stronger versions of the Orlicz-Petty projection inequality
Károly J. Böröczky
We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.
Intrinsic volumes of random polytopes with vertices on the boundary of a convex body
Károly J. Böröczky, Ferenc Fodor, Daniel Hug
Let be a convex body in , let , and let be a positive and continuous probability density function with respect to the -dimensional H…
Stability results for the volume of random simplices
Gergely Ambrus, Károly J. Böröczky
It is known that for a convex body K in R^d of volume one, the expected volume of random simplices in K is minimised if K is an ellipsoid, and for d = 2, maximised if K is a triang…
Stability of some versions of the Prékopa-Leindler inequality
Károly J. Böröczky, Keith M. Ball
Two consequences of the stability version of the one dimensional Prékopa-Leindler inequality are presented. One is the stability version of the Blaschke-Santaló inequality, and the…
The mean width of random polytopes circumscribed around a convex body
Károly J. Böröczky, Ferenc Fodor, Daniel Hug
Let K be a d-dimensional convex body, and let be the intersection of n halfspaces containing whose bounding hyperplanes are independent and identically distributed. U…
The mean width of circumscribed random polytopes
Károly J. Böröczky, Rolf Schneider
For a given convex body K in , a random polytope is defined (essentially) as the intersection of independent closed halfspaces containing and having an isotr…