Mappings with convex potentials and the quasiconformal Jacobian problem

Kovalev, Leonid V.; Maldonado, Diego

Illinois J. Math., Tome 49 (2005) no. 2, p. 1039-1060 / Harvested from Project Euclid

Résumé

This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.

Publié le : 2005-10-15
Classification: 30C65, 26B25, 31B15

@article{1258138126,
     author = {Kovalev, Leonid V. and Maldonado, Diego},
     title = {Mappings with convex potentials and the quasiconformal Jacobian problem},
     journal = {Illinois J. Math.},
     volume = {49},
     number = {2},
     year = {2005},
     pages = { 1039-1060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138126}
}

Kovalev, Leonid V.; Maldonado, Diego. Mappings with convex potentials and the quasiconformal Jacobian problem. Illinois J. Math., Tome 49 (2005) no. 2, pp.  1039-1060. http://gdmltest.u-ga.fr/item/1258138126/