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arXiv · 1511.09167

Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics

Craig van Coevering
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Abstract

We develop some pluripotential theoretic techniques for the transversally holomorphic foliation of a Sasakian manifold. We prove the convexity of the K-energy along weak geodesics for Sasakian manifolds. This implies that the K-energy is bounded below if a constant scalar curvature structure exists with those metrics minimizing it. More generally, a relative version of the K-energy is convex, and bounded below if there exists a Sasaki-extremal metric, providing an important necessary condition for Sasaki-extremal metrics. Another application is a proof of the uniqueness of Sasaki-extremal metrics, for a fixed transversally holomorphic structure on the Reeb foliation.

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Craig van Coevering. 2016-03-24. Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics. https://arxiv.org/abs/1511.09167

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