A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations
A singular Sphere Covering Inequality: uniqueness and symmetry of solutions to singular Liouville-type equations
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DOI：
10.1007/s00208-018-1761-1
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发表时间：
2018-10
影响因子：
1.4
通讯作者：
D. Bartolucci;C. Gui;Aleks Jevnikar;Amir Moradifam
中科院分区：
文献类型：
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作者：
D. Bartolucci;C. Gui;Aleks Jevnikar;Amir Moradifam
我们得到了球面覆盖不等式的一个奇异版本，它是最近在Gui和Moradifam(发明数学)中引入的。Https://doi.org/10.1007/s00222-018-0820-2,2018年)，适用于处理具有超调和权的奇异Liouberle型问题。作为应用，我们得到了球面上和有界域上奇异平均场方程解的新的唯一性结果，以及已有结果的新的自包含的证明，例如在Luo和Tian(Proc am Math Soc116(4)：1119-1129,1992)中首先建立了球面凸多面体的唯一性。此外，我们还得到了球面Onsager涡旋方程的新对称性结果。
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 new uniqueness 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.