# $C^{1,1}$ regularity of geodesics of singular K\"{a}hler metrics

@article{Chu2019C11RO, title={\$C^\{1,1\}\$ regularity of geodesics of singular K\"\{a\}hler metrics}, author={Jianchun Chu and Nicholas McCleerey}, journal={arXiv: Differential Geometry}, year={2019} }

We show the optimal $C^{1,1}$ regularity of geodesics in nef and big cohomology class on K\"ahler manifolds away from the non-K\"ahler locus, assuming sufficiently regular initial data. As a special case, we prove the $C^{1,1}$ regularity of geodesics of K\"ahler metrics on compact K\"ahler varieties away from the singular locus. Our main novelty is an improved boundary estimate for the complex Monge-Amp\`ere equation that does not require strict positivity of the reference form near the…

## 3 Citations

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Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ be a smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$…

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