Regularity of the geodesic equation in the space of Sasakian metrics

Abstract

This paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics. Firstly, we reduce the geodesic equation in the space of Sasakian metrics to a Dirichlet problem of degenerate complex Monge-Ampére type eqution on the Kähler cone; secondly, we obtain a priori etimates for the above equation. These a priori estimates guarantee the existence and uniqueness of $C_w^2$ geodesic for any two points in the space of Sasakian metrics. We also give some geometric applications of the above estimates in the end of this paper.

References in corpus (7)

• The Space of Kähler metrics (II)
• The Monge-Ampère operator and geodesics in the space of Kähler potentials
• Uniqueness and examples of compact toric Sasaki-Einstein metrics
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• A diameter bound for Sasaki manifolds with application to uniqueness for Sasaki-Einstein structure
• The space of volume forms
• On the uniqueness of Sasaki-Einstein metrics

Cited by in corpus (1)

• On the transverse scalar curvature of a compact Sasaki manifold