Concerning the problem of extremality of quasiconformal mappings with dilatation bounds, we discuss the unique extremality of the problem and prove the if part of a conjecture on the unique extremality. To this end, we need to investigate a new extremal problem in the infinitesimal setting. In particular, we give a complete description of the unique infinitesimal extremality of partially zero Beltrami differentials.
@article{1113246383,
author = {Shen, Yu-Liang},
title = {On the unique extremality of quasiconformal mappings with dilatation bounds},
journal = {Tohoku Math. J. (2)},
volume = {56},
number = {1},
year = {2004},
pages = { 105-123},
language = {en},
url = {http://dml.mathdoc.fr/item/1113246383}
}
Shen, Yu-Liang. On the unique extremality of quasiconformal mappings with dilatation bounds. Tohoku Math. J. (2), Tome 56 (2004) no. 1, pp. 105-123. http://gdmltest.u-ga.fr/item/1113246383/