@article{3e72e2e3b4ce4dfd8ad6d191f431398d,
title = "On the [InlineEquation not available: see fulltext.] Regularity of Geodesics in the Space of K{\"a}hler Metrics",
abstract = "We prove that any two K{\"a}hler potentials on a compact K{\"a}hler 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-Amp{\`e}re equation, which is independent of a positive lower bound for the right hand side.",
keywords = "Complex Monge-Ampere equation, Geodesics in the space of Kahler metrics, Real Hessian estimates",
author = "Jianchun Chu and Valentino Tosatti and Ben Weinkove",
note = "Funding Information: The authors thank J. Song for pointing out a simplification of the proof given in an earlier version of this paper, and M. P{\u a}un for interesting discussions. We also thank the referee for some helpful comments. The first-named author would like to thank his advisor G. Tian for encouragement and support.The second-named author was partially supported by NSF Grant DMS-1610278, and the third-named author by NSF Grant DMS-1406164. This work was completed while the second-named author was visiting the Yau Mathematical Sciences Center at Tsinghua University in Beijing, which he would like to thank for the hospitality. Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG.",
year = "2017",
month = dec,
day = "1",
doi = "10.1007/s40818-017-0034-8",
language = "English (US)",
volume = "3",
journal = "Annals of PDE",
issn = "2524-5317",
publisher = "Springer Science + Business Media",
number = "2",
}