We show that there are infinitely many counterexamples to Minkowski’s conjecture in positive
characteristic regarding uniqueness of the upper bound of the multiplicative covering radius,
, by constructing a
sequence of compact
-orbits
where
obtains its conjectured upper bound. In addition, we show that these orbits, as
well as a slightly larger sequence of orbits, must exhibit complete escape of
mass.
Keywords
compact orbit, diagonal group, function fields, positive
characteristic, Minkowski conjecture, geometry of numbers,
covering radius, measures, escape of mass
