A note on Yamabe constants of products with hyperbolic spaces

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We study the Hⁿ-Yamabe constants of Riemannian products (Hⁿ × Mᵐ, gₕⁿ +g), where (M,g) is a compact Riemannian manifold of constant scalar curvature and gₕⁿ is the hyperbolic metric on Hⁿ. Numerical calculations can be carried out due to the uniqueness of (positive, finite energy) solutions of the equation Δu -λu + uq =0 on hyperbolic space Hⁿ under appropriate bounds on the parameters λ, q, as shown by G. Mancini and K. Sandeep. We do explicit numerical estimates in the cases (n,m)=(2,2),(2,3) and (3,2).