Rectifiability of Sets of Finite Perimeter in Carnot Groups: Existence of a Tangent Hyperplane View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-07

AUTHORS

Luigi Ambrosio, Bruce Kleiner, Enrico Le Donne

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∈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. More... »

PAGES

509-540

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12220-009-9068-9

DOI

http://dx.doi.org/10.1007/s12220-009-9068-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031923890


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