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

Jianchun Chu, Valentino Tosatti, Ben Weinkove

Published 2016-11-08Version 1

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.