Schwarz lemma for conical K\"ahler metrics with general cone angles

Abstract

The Schwarz--Pick lemma is a fundamental result in complex analysis. It is well-known that Yau generalized it to the higher dimensional manifolds by applying his maximum principle for complete Riemannian manifolds. Jeffres obtained Schwarz lemma for volume forms of conical K\"ahler metrics, based on a barrier function and the maximum principle argument. In this note, we generalize Jeffres' result to general cone angles including the case when the pullback of the metric would blows up along the divisors.