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Variation of Perimeter Measure in sub-Riemannian geometry

Robert K. Hladky·Scott D. Pauls
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Abstract

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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Robert K. Hladky, Scott D. Pauls. 2007-02-08. Variation of Perimeter Measure in sub-Riemannian geometry. https://arxiv.org/abs/math/0702237

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