A Lehto--Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space

TL;DR

This paper proves a new theorem and rescaling principle for isolated essential singularities of holomorphic curves in complex spaces, aiding in establishing big Picard and Brody theorems.

Contribution

It introduces a Lehto--Virtanen-type theorem and a rescaling principle specifically for isolated essential singularities in complex spaces, advancing complex analysis.

Findings

Established a Lehto--Virtanen-type theorem for holomorphic curves

Developed a rescaling principle for isolated essential singularities

Facilitated proofs of big Picard and Brody theorems in complex spaces

Abstract

We establish a Lehto--Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space, which are useful for establishing a big Picard-type theorem and a big Brody-type one for holomorphic curves.