Resumen de Proof of spherical flocking based on quantitative rearrangement inequalities

Rupert L. Frank, Elliott H. Lieb

• Our recent work on the Burchard–Choksi–Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the char- acteristic 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.