Properties of Carathéodory Measure Hyperbolic Universal Covers of Compact Kahler Manifolds
This article explores some properties of universal covers of compact Kahler 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 Kahler manifolds and the Carathéodory measure of its universal cover (similar result as in [Kikuta 10]). Using similar method, an inequality is established between the restricted volume of canonical bundle of a compact Kahler manifolds and the restricted Carathéodory measure of its covering, solving a conjecture in [Kikuta 13].
Yeung, Purdue University.
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