We show the optimal C1,1regularity of geodesics in nef and big cohomology class on Kähler manifolds away from the non-Kähler locus, assuming sufficiently regular initial data. As a special case, we prove the C1,1regularity of geodesics of Kähler metrics on compact Kähler varieties away from the singular locus. Our main novelty is an improved boundary estimate for the complex Monge-Ampère equation that does not require strict positivity of the reference form near the boundary. We also discuss the case of some special geodesic rays.
|Original language||English (US)|
|State||Published - Jan 7 2019|
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