A Few Remarks about Equality of Indicatrices of Two Functions and a Conjecture

Abstract

Having defined for a couple of functions non co-supportivity in a given direction, we construct for any finite set of directions a couple \(f\) and \(g\) of possibly very regular, continuous except finite many points functions, which in any of these directions are non co-supportive and have the same indicatrix. Adding the requirement that both be continuous (on the joint interval of definition), we are still able to produce such a construction for two directions, but two seems to be the limit: it seems that such a result could not be had for three directions.