We derive a singular version of the Sphere Covering Inequality which was recently introduced in Gui and Moradifam (Invent Math. https://doi.org/10.1007/s00222-018- 0820-2, 2018) suitable for treating singular Liouville-type problems with superharmonic weights. As an application we deduce newuniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains, as well as new self-contained proofs of previously known results, such as the uniqueness of spherical convex polytopes first established in Luo and Tian (Proc Am Math Soc 116(4):1119– 1129, 1992). Furthermore, we derive new symmetry results for the spherical Onsager vortex equation.

Bartolucci, D., Gui, C., Jevnikar, A., Moradifam, A. (2019). A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations. MATHEMATISCHE ANNALEN, 374(3-4), 1883-1922 [10.1007/s00208-018-1761-1].

A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations

D. Bartolucci
Membro del Collaboration Group
;
2019-01-01

Abstract

We derive a singular version of the Sphere Covering Inequality which was recently introduced in Gui and Moradifam (Invent Math. https://doi.org/10.1007/s00222-018- 0820-2, 2018) suitable for treating singular Liouville-type problems with superharmonic weights. As an application we deduce newuniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains, as well as new self-contained proofs of previously known results, such as the uniqueness of spherical convex polytopes first established in Luo and Tian (Proc Am Math Soc 116(4):1119– 1129, 1992). Furthermore, we derive new symmetry results for the spherical Onsager vortex equation.
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Geometric PDEs, Singular Liouville-type equations, Mean field equation, Uniqueness results, Sphere Covering Inequality, Alexandrov-Bol inequality.
partially supported by FIRB project "Analysis and Beyond", by PRIN project 2012, ERC PE1 11, "Variational and perturbative aspects in nonlinear differential problems", and by the Consolidate the Foundations project 2015 (sponsored by Univ. of Rome "Tor Vergata"), "Nonlinear Differential Problems and their Applications".
Bartolucci, D., Gui, C., Jevnikar, A., Moradifam, A. (2019). A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations. MATHEMATISCHE ANNALEN, 374(3-4), 1883-1922 [10.1007/s00208-018-1761-1].
Bartolucci, D; Gui, C; Jevnikar, A; Moradifam, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/205164
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