Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds
Sharp Sobolev-Poincaré inequalities on compact Riemannian manifolds
Given $(M,g)$ a smooth compact Riemannian $n$-manifold, $n \ge 3$, we return in this article to the study of the sharp Sobolev-Poincaré type inequality \begin{equation*}\Vert u\Vert _{2^\star }^2 \le K_n^2\Vert \nabla u\Vert _2^2 + B\Vert u\Vert _1^2\tag *{(0.1)}\end{equation*} where $2^\star = 2n/(n-2)$ is the critical Sobolev exponent, and $K_n$ is …