Quasiconformal geometry of monotone mappings

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21 Scopus citations


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 Holder 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.

Original languageEnglish (US)
Pages (from-to)391-408
Number of pages18
JournalJournal of the London Mathematical Society
Issue number2
StatePublished - Apr 2007
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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