Deformation of Brody curves and mean dimension

TL;DR

This paper develops deformation theory for Brody curves, which are holomorphic maps from the complex plane to projective space, and uses it to establish a lower bound on their mean dimension.

Contribution

It introduces a deformation theory framework for Brody curves in infinite dimensional settings and applies it to analyze their mean dimension.

Findings

Established a lower bound on the mean dimension of Brody curves

Developed deformation theory applicable to infinite dimensional geometric objects

Extended deformation concepts to non-compact domain holomorphic maps

Abstract

The main purpose of this paper is to show that ideas of deformation theory can be applied to "infinite dimensional geometry". We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite dimensional. As an application we prove a lower bound on the mean dimension of the space of Brody curves.