Critical Point Equation on three-dimensional manifolds and the Besse Conjecture

Abstract

In this paper, we present the resolution of the Besse conjecture on a three dimensional compact manifold. We also prove the rigidity of the Miao-Tam critical metric on a three dimensional compact manifold with a smooth boundary.

arXiv commentThere is an error in the proof of Lemma 3.6 (Lemma 5.1)