Properties of Carathéodory measure hyperbolic universal covers of compact Kähler manifolds

Ng, Ngai-Fung

doi:10.1090/proc/14045

Properties of Carathéodory measure hyperbolic universal covers of compact Kähler manifolds
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Proc. Amer. Math. Soc. 146 (2018), 3923-3934 Request permission

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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