ON THE MAXIMIZATION OF A CLASS OF FUNCTIONALS ON CONVEX REGIONS, AND THE CHARACTERIZATION OF THE FARTHEST CONVEX SET
This article considers a family of functionals J to be maximized over the planar convex sets K for which the perimeter and Steiner point have been fixed. Assuming that J is the integral of a positive quadratic expression in the support function h and its derivative, the maximizer is always either a...
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| Veröffentlicht in: | Mathematika 2010-07, Vol.56 (2), p.245-265 |
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| container_title | Mathematika |
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| creator | Harrell II, Evans M. Henrot, Antoine |
| description | This article considers a family of functionals J to be maximized over the planar convex sets K for which the perimeter and Steiner point have been fixed. Assuming that J is the integral of a positive quadratic expression in the support function h and its derivative, the maximizer is always either a triangle or a line segment (which can be considered as a collapsed triangle). Among the concrete consequences of the main theorem is the fact that, given any convex body K1 of finite perimeter, the set in this class that is farthest away in the sense of the L2 distance is always a line segment. The same property is proved for the Hausdorff distance. |
| doi_str_mv | 10.1112/S0025579310000495 |
| format | Article |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | 49Q10 (secondary) 52A10 52A40 (primary) 52B60 Mathematics Metric Geometry |
| title | ON THE MAXIMIZATION OF A CLASS OF FUNCTIONALS ON CONVEX REGIONS, AND THE CHARACTERIZATION OF THE FARTHEST CONVEX SET |
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