Notes on the uniqueness of Type II Yamabe metrics

Abstract

In this paper, we study the uniqueness of type II Yamabe metrics in conformal classes on a compact connected manifold with boundary, and we investigate Obata-type theorems for type II Yamabe metrics. In particular, we establish a theorem which gives a sufficient condition for a metric to be the unique Type II Yamabe metric in its conformal class. We also prove the corresponding theorem for the CR Yamabe problem on closed manifolds.

arXiv comment16 pages. This preprint has not any post-submission improvements or corrections. The Version of Record of this article is published in Nonlinear Differential Equations and Applications NoDEA, and is available online at https://doi.org/10.1007/s00030-025-01092-0