A graph arising in the geometry of numbers (Q2031989)

Recall that the parametric geometry of numbers gave rise to a nice visualisation of the simultaneous approximation properties for \(k\)-tuples of real numbers. Namely, one can consider the combined graph of the related successive minima functions, which is used to detect and to study various inequalities among classical exponents of simultaneous approximation. In particular regular graphs provide extremal cases for some of these inequalities. In this paper the author define and study the first properties of an analogue of regular graphs for the case of weighted simultaneous approximation.