On infinitesimally weakly non-decreasable Beltrami differentials

Abstract

Z. Zhou et al. proved that in a Teichmüller 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.