On infinitesimally weakly non-decreasable Beltrami differentials

TL;DR

This paper proves the existence of a weakly non-decreasable extremal Beltrami differential within an infinitesimal equivalence class, extending previous results on extremal quasiconformal mappings.

Contribution

It establishes the existence of a weakly non-decreasable extremal Beltrami differential in infinitesimal classes, generalizing prior work on extremal quasiconformal maps.

Findings

Existence of weakly non-decreasable extremal Beltrami differentials in infinitesimal classes

Extension of previous results from Teichmüller to infinitesimal settings

Advancement in understanding extremal problems in quasiconformal theory

Abstract

Z. Zhou et al. proved that in a Teichm\"uller equivalence class, there exists an extremal quasiconformal mapping with a weakly non-decreasable dilatation. In this paper, we prove that in an infinitesimal equivalence class, there exists a weakly non-decreasable extremal Beltrami differential.