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.
"Best constants in second-order Sobolev inequalities on compact Riemannian manifolds in the presence of symmetries,"
Turkish Journal of Mathematics: Vol. 36:
4, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss4/11