Geometrical pluripotential theory on Sasaki manifolds

Abstract

We extend profound results in pluripotential theory on Kahler manifolds to Sasaki setting via its transverse Kahler structure. As in Kahler case, these results form a very important piece to solve the existence of Sasaki metrics with constant scalar curvature (cscs) in terms of properness of K-energy. One main result is to generalize T. Darvas' theory on the geometric structure of the space of Kahler potentials in Sasaki setting. Along the way we extend most of corresponding results in pluripotential theory to Sasaki setting via its transverse Kahler structure.

59 pages

References in corpus (4)

• On the constant scalar curvature Kähler metrics, existence results
• On the constant scalar curvature Kähler metrics, general automorphism group
• On the constant scalar curvature Kähler metrics, apriori estimates
• On deformation of extremal metrics

Cited by in corpus (4)

• Algebraicity of the Metric Tangent Cones and Equivariant K-stability
• Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
• Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications
• Positivity in Foliated Manifolds and Geometric Applications