Contact Equations and Lipschitz Extensions

Abstract

We characterize locally Lipschitz mappings and existence of Lipschitz extensions through a first order nonlinear system of PDEs, that we call “contact equations”. As an application, we show the existence of Lipschitz extensions for mappings defined on subsets of the 2-dimensional Euclidean space with values in higher dimensional Heisenberg groups. These results suggest a precise method to tackle Lipschitz extension problems for new couples of groups.

Cite this paper

@inproceedings{Magnani2007ContactEA, title={Contact Equations and Lipschitz Extensions}, author={Valentino Magnani}, year={2007} }