Proof of spherical flocking based on quantitative rearrangement inequalities

• Rupert L. Frank ^[2] ; Elliott H. Lieb ^[1]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] Munich Center for Quantum Science and Technology, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 3, 2021, págs. 1241-1263
• Idioma: inglés
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• Resumen

  • 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.