REAL

Dowker-type theorems for hyperconvex discs

Fejes Tóth, Gábor and Fodor, Ferenc (2015) Dowker-type theorems for hyperconvex discs. Periodica Mathematica Hungarica, 70 (2). pp. 131-144. ISSN 0031-5303 (print), 1588-2829 (online)

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Abstract

A hyperconvex disc of radius r is a planar set with nonempty interior that is the intersection of closed circular discs of radius r . A convex disc-polygon of radius r is a set with nonempty interior that is the intersection of a finite number of closed circular discs of radius r . We prove that the maximum area and perimeter of convex disc- n -gons of radius r contained in a hyperconvex disc of radius r are concave functions of n , and the minimum area and perimeter of disc- n -gons of radius r containing a hyperconvex disc of radius r are convex functions of n . We also consider hyperbolic and spherical versions of these statements.

Item Type: Article
Uncontrolled Keywords: Hyperconvexity; Dowker-type theorems; Disc-polygons; APPROXIMATION
Subjects: Q Science / természettudomány > QA Mathematics / matematika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 17 Feb 2016 10:05
Last Modified: 17 Feb 2016 10:05
URI: http://real.mtak.hu/id/eprint/33619

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