Variation of Perimeter Measure in sub-Riemannian geometry

2007/02/08 by Robert K. Hladky, Hladky, Robert K., Scott D. Pauls +1
Mathematics · #53C17 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C17 #msc:53C42

paper · pdf · doi:10.48550/arxiv.math/0702237

37 pages

arxiv created 2007/02/08 · arxiv updated 2009/12/01

Abstract

We derive a formula for the first variation of horizontal perimeter measure for C² hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For C² hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for variations supported away from the characteristic locus. This variation formula is used to show the bubble sets in \hn2 are stable under volume preserving variations.

Related

• Sub-Finsler Heisenberg Perimeter Measures
• Perimeter on a manifold, with applications to partial differential equations
• Surface measure on, and the local geometry of, sub-Riemannian manifolds
• BV functions and sets of finite perimeter in sub-Riemannian manifolds
• Blow-up estimates at horizontal points and applications