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A Favard‐type problem for 3d convex bodies
Author(s) -
Campi Stefano,
Gronchi Paolo
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn039
Subject(s) - mathematics , convex hull , convex body , mixed volume , surface of revolution , regular polygon , plane (geometry) , perimeter , orthogonal convex hull , constant (computer programming) , combinatorics , geometry , type (biology) , planar , surface (topology) , mathematical analysis , ecology , computer science , biology , programming language , computer graphics (images)
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 ℝ 3 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.