On Yamabe Constants of Products with Hyperbolic Spaces

We study the Hn-Yamabe constants of Riemannian products \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\mathbf{H}^{n} \times M^{m} , g_{h}^{n} +g)$\end{document}, where (M,g) is a compact Riemannian manifold of constant scalar curvature and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$g_{h}^{n}$\end{document} 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).