Large Harnack inequalities, Kobayashi distances and holomorphic motions

TL;DR

This paper generalizes Harnack inequalities for various classes of functions and applies these results to analyze the smoothness of holomorphic motions over almost complex manifolds.

Contribution

It introduces new generalizations of Harnack inequalities and demonstrates their application to the study of holomorphic motions in complex geometry.

Findings

Generalized Harnack inequalities for pluriharmonic, holomorphic, and almost holomorphic functions.

Established smoothness properties of holomorphic motions over almost complex manifolds.

Drawn analogies between classical inequalities and modern complex analysis contexts.

Abstract

We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties of holomorphic motions over almost complex manifolds.