Abstract
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) |
---|---|
Pages (from-to) | 391-408 |
Number of pages | 18 |
Journal | Journal of the London Mathematical Society |
Volume | 75 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2007 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics