• Corpus ID: 119297784

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

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