Non-integrated defect relation for meromorphic mappings from a K\"ahler manifold with hypersurfaces of a projective variety in subgeneral position

TL;DR

This paper develops a new defect relation for meromorphic maps from Kähler manifolds to projective varieties intersecting hypersurfaces in subgeneral position, with explicit truncation levels, extending previous results and applying to Gauss maps of minimal surfaces.

Contribution

It introduces a truncated non-integrated defect relation for meromorphic mappings in subgeneral position, generalizing earlier theorems and providing explicit truncation estimates.

Findings

Generalizes previous defect relations to subgeneral position hypersurfaces.

Provides explicit truncation levels for defect estimates.

Applies results to the distribution of Gauss maps of minimal surfaces.

Abstract

In this paper, we establish a truncated non-integrated defect relation for meromorphic mappings from a complete K\"ahler manifold into a projective variety intersecting a family of hypersurfaces located in subgeneral position, where the truncation level of the defect is explicitly estimated. Our result generalizes and improves previous ones. In particular, when the family of hypersurfaces located in general position, our theorem will implies the previous result of Min Ru-Sogome. In the last part of this paper we will apply ours to study the distribution of the Gauss map of minimal surfaces.