Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane

Details Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane

2008-01-24

arxiv.org/abs/0801.3741v1

Mathematics

Analysis of PDEs

Scientific paper

We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G, then for almost every x in G with respect to the perimeter measure of E, some tangent of E at x is a vertical halfspace. This is a partial extension of a theorem of Franchi-Serapioni-Serra Cassano in step 2 Carnot groups: they have shown that, for almost every x, E has a unique tangent at x, and this tangent is a vertical halfspace.

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