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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