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- Title
A Favard-type problem for 3d convex bodies.
- Authors
Campi, Stefano; Gronchi, Paolo
- Abstract
A theorem due to Favard states that among all plane sets of given area and perimeter, the symmetric lens has maximum circumradius. This paper deals with the higher-dimensional problem of finding the convex body in ℝ3 of given volume and mean width with the largest possible diameter. It is shown that the solution is the convex hull of a surface of revolution with constant Gauss curvature and a segment lying on the axis of revolution. Such a body is conjectured also to maximize the circumradius in the same class.
- Subjects
CONVEX bodies; CONVEX functions; CURVATURE; CALCULUS; CURVES
- Publication
Bulletin of the London Mathematical Society, 2008, Vol 40, Issue 4, p604
- ISSN
0024-6093
- Publication type
Article
- DOI
10.1112/blms/bdn039