On uniqueness and differentiability in the space of Yamabe metrics

2002/10/29 by Michael T. Anderson, Anderson, Michael T. · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.math/0210446

9pp. This is a complete rewritting of the previous version on the same topic, with new title. The reasoning for (2.14) in v1 is incorrect, and this estimate remains an open problem

arxiv created 2005/06/07 · arxiv updated 2009/11/30

Abstract

We prove that generically (positive) Yamabe metrics are unique in their conformal class, and describe some sufficient conditions which imply that a Yamabe metric of locally maximal scalar curvature is an Einstein metric.

Cited by

• The CR Yamabe invariant and constant scalar curvature Sasaki metrics

Related

• A note on the uniqueness of solutions for the Yamabe problem
• Non-Einstein relative Yamabe metrics
• Notes on the uniqueness of Type II Yamabe metrics
• Poincaré-Einstein metrics and Yamabe invariants
• Conformal classes realizing the Yamabe invariant