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Costin Vlcu, Tudor Zamfirescu

Symmetry and the farthest point mapping on convex surfaces

Consider the mapping F associating to each point x of a convex surface the set of all points at maximal intrinsic distance from x. We provide a large class of surfaces on which F is single-valued and involutive. Moreover, we show that there are point-symmetric surfaces of revolution with F single-valued but not involutive.

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 6, 07/2006
Pages: 379 - 387

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