On the C1,1 Regularity of Geodesics in the Space of Kähler Metrics

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Abstract

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 languageEnglish (US)
Article number15
JournalAnnals of Partial Differential Equations
Volume3
Issue number2
StatePublished - 2017

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