We prove that any two Kähler potentials on a compact Kähler manifold can be connected by a geodesic segment of C1,1 regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Ampère equation, which is independent of a positive lower bound for the right hand side.
|Original language||English (US)|
|Journal||Annals of Partial Differential Equations|
|State||Published - 2017|