%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