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- W2751737055 abstract "We prove the existence of a family of blow-up solutions of a mean field equation on sphere. The solutions blow up at four points where the minimum value of a potential energy function (involving the Green's function) is attained. The four blow-up points form a regular tetrahedron. Moreover, the solutions we build have a group of symmetry $T_d$ which is isomorphic to the symmetric group $S_4$. Other families of solutions can be similarly constructed with blow-up points at the vertices of equilateral triangles on a great circle or other inscribed platonic solids (cubes, octahedrons, icosahedrons and dodecahedrons). All of these solutions have the symmetries of the corresponding configuration, while they are non-axially symmetric." @default.
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- W2751737055 date "2017-09-07" @default.
- W2751737055 modified "2023-09-27" @default.
- W2751737055 title "Non-axially symmetric solutions of a mean field equation on $mathbb{S}^2$" @default.
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