Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - B. Kleiner - E. Le Donne

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

created by ambrosio on 23 Jan 2008
modified on 24 Jan 2008

[BibTeX]

Preprint

Inserted: 23 jan 2008
Last Updated: 24 jan 2008

Year: 2008

Abstract:

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 proved that, for almost every $x$, $E$ has a unique tangent at $x$, and this tangent is a halfspace.

Keywords: Carnot groups, Sets of finite perimeter, Rectifiability


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