Rectifiability of Sets of Finite Perimeter in Carnot Groups: Existence of a Tangent Hyperplane |
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Authors: | Luigi Ambrosio Bruce Kleiner Enrico Le Donne |
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Institution: | (1) Scuola Normale Superiore, Pisa, Italy;(2) Yale University, New Haven, USA |
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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.
The second author was partially supported by NSF grant DMS-0701515. |
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Keywords: | Rectifiability Carnot groups Caccioppoli set Sets of finite perimeter |
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