TY - JOUR
T1 - Rectifiability of sets of finite perimeter in carnot groups
T2 - Existence of a tangent hyperplane
AU - Ambrosio, Luigi
AU - Kleiner, Bruce
AU - Le Donne, Enrico
N1 - Funding Information:
The second author was partially supported by NSF grant DMS-0701515.
PY - 2009/7
Y1 - 2009/7
N2 - 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.
AB - 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.
KW - Caccioppoli set
KW - Carnot groups
KW - Rectifiability
KW - Sets of finite perimeter
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U2 - 10.1007/s12220-009-9068-9
DO - 10.1007/s12220-009-9068-9
M3 - Article
AN - SCOPUS:84897998590
SN - 1050-6926
VL - 19
SP - 509
EP - 540
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -