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Properties of Carathéodory measure hyperbolic universal covers of compact Kähler manifolds


Author: Ngai-Fung Ng
Journal: Proc. Amer. Math. Soc. 146 (2018), 3923-3934
MSC (2010): Primary 32Q45
DOI: https://doi.org/10.1090/proc/14045
Published electronically: May 24, 2018
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Abstract: This article explores some properties of universal covers of compact Kähler manifolds under the assumption of Carathéodory measure hyperbolicity. In particular, by comparing invariant volume forms, an inequality is established between the volume of canonical bundle of a compact Kähler manifold and the Carathéodory measure of its universal cover (similar result as in [Proc. Amer. Math. Soc. 139 (2011), pp. 1411-1420]). Using a similar method, an inequality is established between the restricted volume of a canonical bundle of a compact Kähler manifold and the restricted Carathéodory measure of its covering, solving a conjecture in [Michigan Math. J. 62 (2013), pp. 259-292].


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Ngai-Fung Ng
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ngn@purdue.edu

DOI: https://doi.org/10.1090/proc/14045
Received by editor(s): July 6, 2017
Received by editor(s) in revised form: December 4, 2017
Published electronically: May 24, 2018
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society