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.
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The second author was partially supported by NSF grant DMS-0701515.
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Ambrosio, L., Kleiner, B. & Le Donne, E. Rectifiability of Sets of Finite Perimeter in Carnot Groups: Existence of a Tangent Hyperplane. J Geom Anal 19, 509–540 (2009). https://doi.org/10.1007/s12220-009-9068-9
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DOI: https://doi.org/10.1007/s12220-009-9068-9