Inserted: 10 jan 2017
Last Updated: 6 mar 2017
We are concerned with symmetry and uniqueness results for three classes of Liouville-type problems defined on bounded domains arising in geometry and mathematical physics: asymmetric Sinh-Gordon equation, cosmic string equation and Toda system. In the spirit of the Sphere covering inequality we provide a series of results under suitable assumptions on the mass associated to these problems.
Keywords: uniqueness results, Geometric PDEs, Sinh-Gordon equation, Toda system, Cosmic string equation, Sphere covering inequality, Symmetry results