Sobolev trace inequality on manifolds with non-negative Ricci curvature and convex boundary

We study some Sobolev trace inequalities on Riemannian manifolds with boundary. Using an adequate Bochner-Reilly type formula, we obtain some uniqueness result for compact n n -dimensional Riemannian manifolds of non-negative Ricci curvature and strictly convex boundary, where 2 ≤ n ≤ 9 2 n 9. As an application of this result, we derive Sobolev and logarithmic trace inequalities with explicit constants.