| Abstract: |
| Extremals of the Sobolev inequality in the Hyperbolic space satisfies a p-Laplace type equation. In this talk we investigate the radial symmetry of extremals of Sobolev inequality in the hyperbolic space or more generally the positive finite energy solutions of the corresponding Euler Lagrange equation. We prove using the moving plane method that the Solutions are radially symmetric with respect to a point in the hyperbolic space. The crucial ingredient in the proof is the sharp asymptotic estimates on the solution and its gradient at infinity, which depends crucially on a classification result for eigenfunctions of the p-Laplace equation in the hyperbolic space with a desired pole at infinity. This is a joint work with Ramya Datta. |
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