Characterizations of Extremals for some Functionals on Convex Bodies
Characterizations of Extremals for some Functionals on Convex Bodies
Abstract We investigate equality cases in inequalities for Sylvester-type functionals. Namely, it was proven by Campi, Colesanti, and Gronchi that the quantity is maximized by triangles among all planar convex bodies K (parallelograms in the symmetric case). We show that these are the only maximizers, a fact proven by Giannopoulos …