Rectifiability of Sets of Finite Perimeter in Carnot Groups: Existence of a Tangent Hyperplane
By Luigi Ambrosio, Bruce Kleiner, Enrico Le Donne. 2008
68 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2dbd073143ebbb523ba27a0828b1bd8393ca7661
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In Applied Mathematics
- Francesco Serra Cassano
- Manuel Ritor'e
- Raul Paolo Serapioni
- P. Mattila
- Valentino Magnani
- Bruno Franchi
- Luigi Ambrosio
- Scott D. Pauls
In Geometry and Topology
- Francesco Serra Cassano
- Manuel Ritor'e
- Raul Paolo Serapioni
- P. Mattila
- Valentino Magnani
- Bruno Franchi
- Jun-cheng Wei
- Davide Vittone
Citations in the corpus
- Characterizations of intrinsic rectifiability in Heisenberg groups (2010, methodology): “In [14,15], (2n,H)-rectifiable sets were used to establish De Giorgi’s structure theory for sets of finite perimeter in step 2 Carnot groups, see also [3] for more general Carnot groups.”
- Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, background): “The importance of tangent cones has been recently stressed in [1].”