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 language||English (US)|
|Number of pages||18|
|Journal||Journal of the London Mathematical Society|
|State||Published - Apr 2007|
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