  Our recent work on the Burchard-Choksi-Topaloglu flocking problem showed that
in the large mass regime the ground state density profile is the characteristic
function of some set. Here we show that this set is, in fact, a round ball. The
essential mathematical structure needed in our proof is a strict rearrangement
inequality with a quantitative error estimate, which we deduce from recent deep
results of M. Christ.
