Published September 27, 2021
| Submitted
Journal Article
Open
Proof of spherical flocking based on quantitative rearrangement inequalities
- Creators
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Frank, Rupert L.
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Lieb, Elliott H.
Chicago
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Abstract
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.
Additional Information
© 2021 Scuola Normale Superiore. Received September 10, 2019; accepted in revised form May 05, 2020. Published online September 2021. Partial support through US National Science Foundation grant DMS-1363432 and through German Research Foundation grant EXC-2111 390814868 (R.L.F.) is acknowledged.Attached Files
Submitted - 1909.04595.pdf
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Additional details
- Eprint ID
- 112128
- Resolver ID
- CaltechAUTHORS:20211201-160010515
- NSF
- DMS-1363432
- Deutsche Forschungsgemeinschaft (DFG)
- EXC-2111 390814868
- Created
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2021-12-01Created from EPrint's datestamp field
- Updated
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2021-12-01Created from EPrint's last_modified field