Lángi, Zsolt and Naszódi, Márton and Talata, István (2012) Ball and spindle convexity with respect to a convex body. Aequationes Mathematicae, 85 (12). pp. 4167. ISSN 00019054 (print version), 14208903 (electronic version)

Text
paper.pdf Download (417kB)  Preview 
Abstract
Let C⊂R^n be a convex body. We introduce two notions of convexity associated to C. A set K is Cball convex if it is the intersection of translates of C, or it is either ∅ , or R^n . The Cball convex hull of two points is called a Cspindle. K is Cspindle convex if it contains the Cspindle of any pair of its points. We investigate how some fundamental properties of conventional convex sets can be adapted to Cspindle convex and Cball convex sets. We study separation properties and Carathéodory numbers of these two convexity structures. We investigate the basic properties of arcdistance, a quantity defined by a centrally symmetric planar disc C, which is the length of an arc of a translate of C, measured in the Cnorm that connects two points. Then we characterize those ndimensional convex bodies C for which every Cball convex set is the Cball convex hull of finitely many points. Finally, we obtain a stability result concerning covering numbers of some Cball convex sets, and diametrically maximal sets in ndimensional Minkowski spaces.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria 
Depositing User:  Dr. Zsolt Lángi 
Date Deposited:  11 Sep 2015 11:09 
Last Modified:  11 Sep 2015 11:09 
URI:  http://real.mtak.hu/id/eprint/26367 
Actions (login required)
View Item 