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arXiv · 1901.02105

$C^{1,1}$ regularity of geodesics of singular Kähler metrics

Jianchun Chu·Nicholas McCleerey
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Abstract

We show the optimal $C^{1,1}$ regularity 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 $C^{1,1}$ regularity 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.

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Jianchun Chu, Nicholas McCleerey. 2020-12-09. $C^{1,1}$ regularity of geodesics of singular Kähler metrics. https://doi.org/10.1112/jlms.12424

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