5 papers
From Blaschke--Santaló-type inequalities to uniform contractions
Károly Bezdek
In this short note, we establish Blaschke--Santaló-type inequalities for -ball bodies. Building on these inequalities, we somewhat further extend earlier results on analogues o…
On basic -ball polyhedra
Károly Bezdek
This note introduces the class of basic -ball polyhedra in the -dimensional Euclidean space for and . We investigate their face structure and, for…
Notes on non-separable arrangements of convex bodies
Károly Bezdek, Zsolt Lángi
A problem posed by ErdÅs in 1945 initiated the study of non-separable arrangements of convex bodies. A finite collection of convex bodies in Euclidean -space is called a non-se…
Selected topics from the theory of intersections of balls
Károly Bezdek, Zsolt Lángi, Márton Naszódi
In this survey, we discuss volumetric and combinatorial results concerning (mostly finite) intersections or unions of balls (mostly of equal radii) in the -dimensional real vect…
On separability in discrete geometry
Károly Bezdek, Zsolt Lángi
A problem of ErdÅs (Amer. Math. Monthly 52: 494-498, 1945) and a theorem of Fejes Tóth and Fejes Tóth (Acta Math. Acad. Sci. Hungar. 24: 229-232, 1973) initiated the study of no…