Calculus of Variations and Geometric Measure Theory

V. Magnani

Differentiability and Area formula on Stratified Lie groups

created on 15 Mar 2000
modified on 24 Jan 2002


Published Paper

Inserted: 15 mar 2000
Last Updated: 24 jan 2002

Journal: Houston J. Math.
Volume: 27
Number: 2
Pages: 297-323
Year: 2001


We prove the Area Formula for Lipschitz maps between stratified nilpotent Lie groups. One of the main tools is the differentiablity of Lipschitz maps, proved by P. Pansu in Ann. of Math. '89. This result is extended to the case of measurable domains with non trivial technical modifications. We study the algebraic properties of differential maps, called G-linear maps. We also give a suitable notion of jacobian for G-linear maps, finding relations with the classical algebraic definition of jacobian. Finally we get the Area formula in this setting, which generalizes the euclidean one to sub-Riemannian, non abelian Lie groups.

Keywords: area formula, stratified groups, differentiability