%0 Journal Article
%@ 0031-5303
%A  Fejes Tóth Gábor
%A  Fodor Ferenc
%A Bolyai Intézet (Matematikai Intézet) SZTE / TTIK MI [2016-],
%A Geometria MTA RAMKI [1955-],
%A MTA Rényi Alfréd Matematikai Kutatóintézet [1955-],
%D 2015
%F publicatio:16252
%J PERIODICA MATHEMATICA HUNGARICA
%N 2
%P 131-144
%T Dowker-type theorems for hyperconvex discs
%U http://publicatio.bibl.u-szeged.hu/16252/
%V 70
%X 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.
%Z WoS:hiba:000354204100001 2019-03-03 00:49 első szerző nem egyezik