Notes on the uniqueness of Type II Yamabe metrics
Differential Geometry
2025-06-24 v1
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.
Keywords
Cite
@article{arxiv.2506.17876,
title = {Notes on the uniqueness of Type II Yamabe metrics},
author = {Shota Hamanaka and Pak Tung Ho},
journal= {arXiv preprint arXiv:2506.17876},
year = {2025}
}
Comments
16 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