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.
"On infinitesimally weakly non-decreasable Beltrami differentials." Kodai Math. J. 43 (2) 339 - 348, June 2020. https://doi.org/10.2996/kmj/1594313557