Nevanlinna theory on complete K\"ahler manifolds

TL;DR

This paper extends Nevanlinna theory to complete Kähler manifolds, establishing a defect relation for holomorphic mappings into complex projective manifolds under specific growth conditions.

Contribution

It introduces a new Nevanlinna theory framework on complete Kähler manifolds and proves a defect relation for holomorphic maps with growth constraints.

Findings

Established a defect relation for holomorphic maps

Extended Nevanlinna theory to non-positively curved Kähler manifolds

Provided growth conditions under which the defect relation holds

Abstract

We study Nevanlinna theory on complete K\"ahler manifolds. As a consequence of the main result, we prove a defect relation of holomorphic mappings from complete K\"ahler manifolds of non-positive sectional curvature into complex projective manifolds under certain growth condition.