On the $C^{1,1}$ regularity of geodesics in the space of Kähler metrics

Abstract

We prove that any two Kahler potentials on a compact Kahler manifold can be connected by a geodesic segment of C^{1,1} regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Ampere equation, which is independent of a positive lower bound for the right hand side.

12 pages; final version to appear in Annals of PDE

References in corpus (2)

• Approximation of weak geodesics and subharmonicity of Mabuchi energy
• On the Maximal Rank Problem for the Complex Homogeneous Monge-Ampère Equation

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