[00698] Rigidity for Sobolev inequalities and radial PDEs on Cartan-Hadamard manifolds
Session Time & Room : 2E (Aug.22, 17:40-19:20) @G402
Type : Contributed Talk
Abstract : We aim at classifying all the Cartan-Hadamard manifolds supporting an optimal function for the $p$-Sobolev inequality. We prove that, under the validity of the Cartan-Hadamard conjecture, which is known to be true in dimension $n\le 4$, the only such manifold is $\mathbb{R}^n$, up to isometries. We also investigate radial solutions to the related $p$-Laplace Lane-Emden equation, obtaining rigidity of finite-energy solutions regardless of optimality. Furthermore, we study the asymptotic behavior of infinite-energy solutions.
