Premium
Volumes of projection bodies
Author(s) -
Brannen Noah Samuel
Publication year - 1996
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557930001175x
Subject(s) - mathematics , simplex , combinatorics , regular polygon , mixed volume , counterexample , subclass , affine transformation , convex body , conjecture , upper and lower bounds , class (philosophy) , convex analysis , invariant (physics) , pure mathematics , convex optimization , mathematical analysis , geometry , artificial intelligence , computer science , antibody , immunology , mathematical physics , biology
C. M. Petty has conjectured the minimum value for a certain affine‐invariant functional denned on the class of convex bodies. We give sharp bounds for this functional on a certain subclass of convex bodies, and we give a counterexample to an upper bound proposed by R. Schneider for the class of centrally symmetric convex bodies. We conjecture that the simplex provides the maximum on the class of all convex bodies, while the largest centrally symmetric subset of a simplex gives a sharp upper bound on the class of all centrally symmetric convex bodies.