Quasiconformal Geometry of Monotone Mappings
نویسنده
چکیده
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.
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