Notes on the uniqueness of Type II Yamabe metrics

2025/06/22 by Hamanaka, Shota, Ho, Pak Tung · 1 citation
#53C18 Secondary #53C21 #58J32 #Differential Geometry (math.DG) #FOS: Mathematics #Primary

paper · doi:10.48550/arxiv.2506.17876

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.

Citations

• Non-Einstein relative Yamabe metrics
• Spectral geometry of the Steklov problem

Cited by

• Existence and Regularity of Extremal Metrics for the Conformal Dirichlet-to-Robin Map

Related

• A note on the uniqueness of solutions for the Yamabe problem
• On uniqueness and differentiability in the space of Yamabe metrics
• A generalization of Aubin's result for a Yamabe-type problem on smooth metric measure spaces
• Conformal classes realizing the Yamabe invariant
• On bifurcation of solutions of the Yamabe problem in product manifolds