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Journal of the London Mathematical Society Advance Access originally published online on April 25, 2007
Journal of the London Mathematical Society 2007 75(2):391-408; doi:10.1112/jlms/jdm008
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© 2007 London Mathematical Society

Quasiconformal geometry of monotone mappings

Leonid V. Kovalev

Department of Mathematics
Texas A&M University
College Station TX 77843-3368
USA

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.

lkovalev{at}math.tamu.edu

2000 Mathematics Subject Classification 47H05 (primary), 30C65, 35J15 (secondary).

Received September 11, 2005; revised July 4, 2006; published online April 25, 2007.


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