Dowker-type theorems for hyperconvex discs
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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2015
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| Sorozat: | PERIODICA MATHEMATICA HUNGARICA
70 No. 2 |
| doi: | 10.1007/s10998-014-0071-y |
| mtmt: | 2488534 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/16252 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 131-144 |
| ISSN: | 0031-5303 |