Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications

Abstract

We prove a priori estimates for a class of transverse fully nonlinear equations on Sasakian manifolds and give some geometric applications such as the transversion Calabi-Yau theorem for transverse balanced and (strongly) Gauduchon metrics. We also explain that similar results hold on compact oriented, taut, transverse Hermitian foliated manifold of complex co-dimension $n$, and give some geometric applications such as the transverse Calabi-Yau theorems for transverse Hermitian and (strongly) Gauduchon metrics.

arXiv comment46 pages,minor typos correction,final version to appear in Advances in Mathematics

References in corpus (18)

• Sasaki-Einstein Manifolds and Volume Minimisation
• The complex Monge-Ampère equation on compact Hermitian manifolds
• The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold
• Second Order Estimates and Regularity for Fully Nonlinear Elliptic Equations on Riemannian Manifolds
• Gauduchon metrics with prescribed volume form
• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• Sasaki-Einstein metrics and K-stability
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Hermitian metrics, (n-1, n-1) forms and Monge-Ampère equations
• The Monge-Ampère equation for non-integrable almost complex structures
• Hessian equations on closed Hermitian manifolds
• On the convergence and singularities of the J-flow with applications to the Mabuchi energy
• A foliated Hitchin-Kobayashi correspondence
• $C^{2,\alpha }$ regularities and estimates for nonlinear elliptic and parabolic equations in geometry
• A parabolic Monge-Ampère type equation of Gauduchon metrics
• Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
• On the sharp dimension estimate of CR holomorphic functions in Sasakian Manifolds
• Geometrical pluripotential theory on Sasaki manifolds

Cited by in corpus (3)

• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures
• The Wu-Yau theorem on Sasakian manifolds
• Positivity in Foliated Manifolds and Geometric Applications