Best constants in second-order Sobolev inequalities on compact Riemannian manifolds in the presence of symmetries

Authors: MOHAMMED ALI

Abstract: Let (M,g) be a smooth compact 3\leq n-dimensional Riemannian manifold, and G a subgroup of the isometry group of (M,g). We establish the best constants in second-order for a Sobolev inequality when the functions are G-invariant.

Keywords: Best constants, compact Riemannian manifolds, Sobolev inequalities, isometries

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