Nevanlinna-type theory based on heat diffusion

TL;DR

This paper develops a Nevanlinna-type theory for holomorphic mappings from certain Kähler manifolds into complex projective manifolds, using heat diffusion to establish defect relations under curvature conditions.

Contribution

It introduces a heat diffusion-based Nevanlinna theory for holomorphic maps from complete Kähler manifolds, extending classical value distribution theory.

Findings

Derived a Nevanlinna-type defect relation using heat diffusion.

Established conditions under which the defect relation holds.

Extended classical theory to a broader geometric setting.

Abstract

We obtain an analogue of Nevanlinna theory of holomorphic mappings from a complete and stochastically complete K\"ahler manifold into a complex projective manifold. When certain curvature conditions are imposed, the Nevanlinna-type defect relation based on heat diffusion is derived.