Rectifiability of sets of finite perimeter in carnot groups: Existence of a tangent hyperplane

Luigi Ambrosio, Bruce Kleiner, Enrico Le Donne

Research output: Contribution to journalArticlepeer-review

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 ε 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 show in Math. Ann. 321, 479-531, 2001 and J. Geom. Anal. 13, 421-466, 2003 that, for almost every x, E has a unique tangent at x, and this tangent is a vertical halfspace.

Original languageEnglish (US)
Pages (from-to)509-540
Number of pages32
JournalJournal of Geometric Analysis
Volume19
Issue number3
DOIs
StatePublished - Jul 2009

Keywords

  • Caccioppoli set
  • Carnot groups
  • Rectifiability
  • Sets of finite perimeter

ASJC Scopus subject areas

  • Geometry and Topology

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