Isoperimetric regions in spherical cones and Yamabe constants of $M\times S^1$

Abstract

Given closed Riemannian manifold $(M^n,g)$ of positive Ricci curvature $Ricci(g)\ge (n-1)g$ we study isoperimetric regions on the spherical cone over $M$. When $g$ is Einstein we use this to compute the Yamabe constant of $(M\times \mathbf{R},g+d{t}^2)$ and so to obtain lower bounds for the Yamabe invariant of $M\times S^1$.

14 pages, new references and a simplification of section 2

Cited by in corpus (2)

• On metrics of positive Ricci curvature conformal to MxR^m
• Results on the existence of the Yamabe minimizer of M^m \times R^n