On the Yamabe constants of product manifolds

2025/11/01 by Sung, Chanyoung
#53C21 #58E99 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.00398

Abstract

By using the fiberwise spherical symmetrization we give a comparison theorem of Yamabe constants on warped products and prove the existence of radially-symmetric Yamabe minimizers on Riemannian manifolds given by products with round spheres.

Citations

• Fiberwise symmetrizations for variational problems on fibred manifolds
• The Weyl functional on 4-manifolds of positive Yamabe invariant
• A note on solutions of Yamabe-type equations on products of spheres
• Isoperimetric profile comparisons and Yamabe constants
• Ricci curvature and conformality of Riemannian manifolds to spheres
• On Yamabe constants of Riemannian products
• Ricci curvature and Yamabe constants
• 3-Manifolds with Yamabe invariant greater than that of \RP³
• Yamabe Invariants and Spin^c Structures
• Yamabe Constants and the Perturbed Seiberg-Witten Equations

Related

• Results on the existence of the Yamabe minimizer of M^m × Rⁿ
• Non-existence of Yamabe minimizers on singular spheres
• A variational analysis of the spinorial Yamabe equation on product manifolds
• On Yamabe constants of Riemannian products
• A Variational Approach to the Yamabe Problem: Conformal Transformations and Scalar Curvature on Compact Riemannian Manifolds