Variation of Perimeter Measure in sub-Riemannian geometry

Details Variation of Perimeter Measure in sub-Riemannian geometry Variation of Perimeter Measure in sub-Riemannian geometry

2007-02-08

arxiv.org/abs/math/0702237v1

Mathematics

Differential Geometry

37 pages

Scientific paper

We derive a formula for the first variation of horizontal perimeter measure for $C^2$ hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For $C^2$ 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 \hn{2} are stable under volume preserving variations.

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