Abstract
We give a survey of our recent work describing a method which combines the Sasaki join construction with the admissible Kähler construction of to obtain new extremal and new constant scalar curvature Sasaki metrics, including Sasaki-Einstein metrics. The constant scalar curvature Sasaki metrics also provide explicit solutions to the CR Yamabe problem. In this regard we give examples of the lack of uniqueness when the Yamabe invariant is positive.
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