Variation of Perimeter Measure in sub-Riemannian geometry
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 2 are stable under volume preserving variations.
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