2007/11/30 by Valentino Magnani, Magnani, Valentino · 1 citation
Mathematics · #22E30 #53C17 #58C25 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.0711.5003
openalex publication_date 2007/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize locally Lipschitz mappings and existence of Lipschitz extensions through a first order nonlinear system of PDEs. We extend this study to graded group-valued Lipschitz mappings defined on compact Riemannian manifolds. Through a simple application, we emphasize the connection between these PDEs and the Rumin complex. We introduce a class of 2-step groups, satisfying some abstract geometric conditions and we show that Lipschitz mappings taking values in these groups and defined on subsets of the plane admit Lipschitz extensions. We present several examples of these groups, called Allcock groups, observing that their horizontal distribution may have any codimesion. Finally, we show how these Lipschitz extensions theorems lead us to quadratic isoperimetric inequalities in all Allcock groups.