On the min-max width of unit volume three-spheres

Abstract

How large can be the width of Riemannian three-spheres of the same volume in the same conformal class? If a maximum value is attained, how does a maximising metric look like? What happens as the conformal class changes? In this paper, we investigate these and other related questions, focusing on the context of Simon-Smith min-max theory.

30 pages. Added word in title for the sake of clarity. Minor typo corrected, a reference added. Submitted