Geometric inequalities in Carnot groups

Francescopaolo Montefalcone

Vol. 263 (2013), No. 1, 171–206

DOI: 10.2140/pjm.2013.263.171

Abstract

Let 𝔾 be a subriemannian k-step Carnot group of homogeneous dimension Q. We prove several geometric inequalities concerning smooth hypersurfaces (submanifolds of codimension one) immersed in  𝔾, endowed with the H-perimeter measure.

Keywords

Carnot groups, subriemannian geometry, hypersurfaces, geometric inequalities

Mathematical Subject Classification 2010

Primary: 49Q15

Secondary: 46E99, 43A80

Milestones

Received: 28 March 2012

Revised: 1 October 2012

Accepted: 19 October 2012

Published: 14 May 2013