Variation of Perimeter Measure in Sub-riemannian Geometry
نویسندگان
چکیده
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. When the manifold admits dilations, we establish a sub-Riemannian Minkowski formula. For C2 hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for variations supported away from the characteristic locus.
منابع مشابه
BV functions and sets of finite perimeter in sub-Riemannian manifolds
We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms Gp : TpM → [0,∞] are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets ...
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