On the structure of finite perimeter sets in step 2 Carnot groups

By Bruno Franchi, Raul Paolo Serapioni, Francesco Serra Cassano. 2003

239 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/1042a8815091ba213082bf512f2f3c79b0030215

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups (2003, methodology): “By the way, as for De Giorgi’s rectifiability theory in general Carnot groups, the problem is far from be fully settled, even if a positive answer is given in [ 23 ] for a large class of Carnot groups containing all step 2 groups.”
Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, unknown): “The following is only a partial list of references [1–3,6, 14–16,26,28,43–45,48,49,56,74,84,85,90].”
Regular submanifolds, graphs and area formula in Heisenberg groups (2007, unknown): “Appendix: Federer-Fleming Currents 42 References 47”
Compensated compactness for differential forms in Carnot groups and applications (2010, background): “,Xm1 have polynomial coefficients (see [11], Proposition 2.”
Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs (2009, background): “In fact, in [17] classical De Giorgi’s rectifiability and divergence theorem for sets of finite perimeter have been fully extended to a Carnot group of step 2 (see also [23]).”
IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES (2006, unknown): “Mathematics Subject Classification 2000: 53C17, 17B66, 43A80”
Intrinsic regular hypersurfaces in Heisenberg groups (2006, methodology): “... introduced: A set S C H n is said (Q - 1)dimensional H-rectifiable if there exists a sequence of H-regular surfaces (Si)i in ]HI n such that ,sQ-1 (S \ UicNSi) = O. This intrinsic notion of rectifiability has been proven particularly useful to obtain in [27] an analog of De Giorgi's structure th”
Geometry of Carnot-Caratheodory Spaces, Differentiability, Coarea and Area Formulas (2009, unknown): “Serra Cassano [56, 57, 58, 59], N.”
A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries (2018, methodology): “Other results that have been generalized are the Isoperimetric Inequality [82], the Poincaré Inequality [52], the Nash Embedding Theorem [60], theMyers-SteenrodRegularity Theorem [32], and, at least partially, theDe-Giorgi Structure Theorem [37].”
Characteristic points, rectifiability and perimeter measure on stratified groups (2006, methodology): “4 of [29], for every > 0 and every R > 0 there exists CR > 0 such that H q+ (E) CRH j j(E); (26)”
Harnack inequality for fractional sub-Laplacians in Carnot groups (2012, background): “We refer to [20], [17], [19], [18] for a detailed presentation.”
TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS (2007, background): “Then the triangle inequality joined with (6) gives us β > 0 and an open set U such that d ( f(x), f(y) ) ≥ β d(x, y), whenever x, y ∈ U and x̄ ∈ U ⊂ U ′.”