General Schwarz Lemmata and their applications

TL;DR

This paper develops generalized Schwarz lemmas that interpolate between existing estimates, offering new insights into the geometry of compact Kähler manifolds with specific curvature conditions.

Contribution

It introduces more flexible Schwarz lemma estimates that unify and extend previous results, enhancing understanding of geometric properties of Kähler manifolds.

Findings

New interpolating estimates for Schwarz lemmas

Applications to algebraic geometry of Kähler manifolds

Enhanced understanding of curvature conditions

Abstract

We prove estimates interpolating the Schwarz Lemmata of Royden-Yau and the ones recently established by the author. These more flexible estimates provide additional information on (algebraic) geometric aspects of compact K\"ahler manifolds with nonnegative holomorphic sectional curvature, nonnegative $\Ric_\ell$ or positive $S_\ell$.