Add to ORKGAbstract. With any given convex body we associate three numbers that exhibit, respectively, its deviation from a ball, a centrally symmetric body, and a body of constant width. Several properties of these deviation measures are studied. Then, noting that these special bodies may be defined in terms of their normals, corresponding deviation measures for normals are introduced. Several inequalities are proved that show that convex bodies cannot deviate much from these special types if their corresponding deviations of the normals are small. These inequalities can be interpreted as stability results. 1
The standard normal distribution on d satisfies ∂Cε ≤ cdε, for all ε> 0 and for all convex su...
Abstract. The Busemann-Petty problem asks whether symmetric con-vex bodies in Rn with smaller (n − 1...
Abstract. The second theorem of Minkowski establishes a relation between the successive minima and t...
Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to smal...
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, cont...
AbstractWe give a different proof of a recent result of Klartag [B. Klartag, A central limit theorem...
AbstractBy using the method of mixed volumes, we give sharp bounds for inclusion measures of convex ...
We consider the convex hull of a finite sample of i.i.d. points uniformly distributed in a convex bo...
Abstract. Let C ⊂ Rn be a convex body. We introduce two notions of convexity associated to C. A set ...
In this paper, several inequalities for inclusion measures of convex bodies were obtained. The inclu...
This thesis consists of four papers about the Minkowski measure of asymmetry and the Minkowski (or B...
AbstractThis paper proposes and compares several ways of measuring the degree of normality of a conv...
The paper deals with the following question: Among the convex plane sets of fixed isoperimetric defi...
In this paper we study properties of sections of convex bodies with respect to the Gaussian measure....
Abstract. A translation body of a convex body is the convex hull of two of its translates intersecti...
The standard normal distribution on d satisfies ∂Cε ≤ cdε, for all ε> 0 and for all convex su...
Abstract. The Busemann-Petty problem asks whether symmetric con-vex bodies in Rn with smaller (n − 1...
Abstract. The second theorem of Minkowski establishes a relation between the successive minima and t...
Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to smal...
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, cont...
AbstractWe give a different proof of a recent result of Klartag [B. Klartag, A central limit theorem...
AbstractBy using the method of mixed volumes, we give sharp bounds for inclusion measures of convex ...
We consider the convex hull of a finite sample of i.i.d. points uniformly distributed in a convex bo...
Abstract. Let C ⊂ Rn be a convex body. We introduce two notions of convexity associated to C. A set ...
In this paper, several inequalities for inclusion measures of convex bodies were obtained. The inclu...
This thesis consists of four papers about the Minkowski measure of asymmetry and the Minkowski (or B...
AbstractThis paper proposes and compares several ways of measuring the degree of normality of a conv...
The paper deals with the following question: Among the convex plane sets of fixed isoperimetric defi...
In this paper we study properties of sections of convex bodies with respect to the Gaussian measure....
Abstract. A translation body of a convex body is the convex hull of two of its translates intersecti...
The standard normal distribution on d satisfies ∂Cε ≤ cdε, for all ε> 0 and for all convex su...
Abstract. The Busemann-Petty problem asks whether symmetric con-vex bodies in Rn with smaller (n − 1...
Abstract. The second theorem of Minkowski establishes a relation between the successive minima and t...