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Quasiconformal geometry of monotone mappings
Author(s) -
Kovalev Leonid V.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm008
Subject(s) - monotone polygon , geometry , mathematics , pure mathematics
This paper concerns a class of monotone mappings, in a Hilbert space, that can be viewed as a nonlinear version of the class of positive invertible operators. Such mappings are proved to be open, locally Hölder continuous, and quasisymmetric. They arise naturally from the Beurling–Ahlfors extension and from Brenier's polar factorization and find applications in the geometry of metric spaces and the theory of elliptic partial differential equations.