On Yamabe constants of Riemannian products

2006/03/20 by Akutagawa, Kazuo, Florit, Luis A., Petean, Jimmy · 1 citation
#53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0603486

Abstract

For a closed Riemannian manifold (M^m,g) of constant positive scalar curvature and any other closed Riemannian manifold (Nⁿ,h), we show that the limit of the Yamabe constants of the Riemannian products (M× N,g+rh) as r goes to infinity is equal to the Yamabe constant of (M^m × Rⁿ, [g+g_E]) and is strictly less than the Yamabe invariant of S^m+n provided n≥ 2. We then consider the minimum of the Yamabe functional restricted to functions of the second variable and we compute the limit in terms of the best constants of the Gagliardo-Nirenberg inequalities.

Cited by

• On the Yamabe constants of product manifolds

Related

• Second Yamabe Constant on Riemannian Products
• A note on Yamabe constants of products with hyperbolic spaces
• Results on the existence of the Yamabe minimizer of M^m × Rⁿ
• Multiplicity results for the Yamabe equation by Lusternik-Schnirelmann\n theory
• Ricci curvature and Yamabe constants