Add to ORKGA translation body of a convex body is the convex hull of two of its translates intersecting each other. In the 1950s, Rogers and Shephard found the extremal values, over the family of n-dimensional convex bodies, of the maximal volume of the translation bodies of a given convex body. In our paper, we introduce a normed version of this problem, and for the planar case, determine the corresponding quantities for the four types of volumes regularly used in the literature: Busemann, Holmes-Thompson, and Gromov's mass and mass*. We examine the problem also for higher dimensions, and for centrally symmetric convex bodies
In this paper we present some notions and classical results from convex geometry which have found nu...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
For a convex body K in Rn, the volume quotient is the ratio of the smallest volume of the circumscri...
Abstract. A translation body of a convex body is the convex hull of two of its translates intersecti...
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Eu...
Abstract. In this note we examine the volume of the convex hull of two congruent copies of a convex ...
The largest volume ratio of a given convex body K ⊂ Rn is defined as lvr(K) := sup L⊂Rn vr(K, L), wh...
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bod...
According to a classical result of Grünbaum, the transversal number τ(F) of any family F of pairwis...
Algorithmic problems in geometry often become tractable with the assumption of convexity. Optimizati...
AMS subject classification: 52A01, 13C99.The algebraic properties of the convex bodies are studied. ...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
In this paper we will explore the interaction between convex geometry and proba-bility in the study ...
We study metric properties of convex bodies B and their polars B0, where B is the convex hull of an...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
In this paper we present some notions and classical results from convex geometry which have found nu...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
For a convex body K in Rn, the volume quotient is the ratio of the smallest volume of the circumscri...
Abstract. A translation body of a convex body is the convex hull of two of its translates intersecti...
In this note we examine the volume of the convex hull of two congruent copies of a convex body in Eu...
Abstract. In this note we examine the volume of the convex hull of two congruent copies of a convex ...
The largest volume ratio of a given convex body K ⊂ Rn is defined as lvr(K) := sup L⊂Rn vr(K, L), wh...
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bod...
According to a classical result of Grünbaum, the transversal number τ(F) of any family F of pairwis...
Algorithmic problems in geometry often become tractable with the assumption of convexity. Optimizati...
AMS subject classification: 52A01, 13C99.The algebraic properties of the convex bodies are studied. ...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
In this paper we will explore the interaction between convex geometry and proba-bility in the study ...
We study metric properties of convex bodies B and their polars B0, where B is the convex hull of an...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
In this paper we present some notions and classical results from convex geometry which have found nu...
In this paper we prove a series of Rogers–Shephard type inequalities for convex bodies when dealing ...
For a convex body K in Rn, the volume quotient is the ratio of the smallest volume of the circumscri...
