Conformal classes realizing the Yamabe invariant

Abstract

We give a characterization of conformal classes realizing a compact manifold's Yamabe invariant. This characterization is the analogue of an observation of Nadirashvili for metrics realizing the maximal first eigenvalue, and of Fraser and Schoen for metrics realizing the maximal first Steklov eigenvalue.

arXiv comment11 pages. An error in Thm 1.1 is corrected, and some typos fixed