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.

A Favard type problem for 3-d convex bodies / S. CAMPI; P. GRONCHI. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - STAMPA. - 40:(2008), pp. 604-612. [10.1112/blms/bdn039]

A Favard type problem for 3-d convex bodies

GRONCHI, PAOLO
2008

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 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.
2008
40
604
612
S. CAMPI; P. GRONCHI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/253011
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