Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group

By B. Kirchheim, Francesco Serra Cassano. 2004

104 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b011f3ee6901e7e0b4ee8657aa0ccf2a9309f880

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Citations in the corpus

TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS (2007, background): “In the same work [ 33 ], the authors provide through a nontrivial construction an example of (H1, R)-regular set of H1 of Euclidean Hausdorff dimension 5/2, that is clearly not rectifiable in the Fed-”
Geometry of Carnot-Caratheodory Spaces, Differentiability, Coarea and Area Formulas (2009, unknown): “Serra Cassano [92], V.”
Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups (2003, background): “Indeed, not only the Euclidean normal can fail to exist almost everywere, but even the Euclidean metric dimension of the boundary could exceed n−1, so making the right hand side of (14) divergent for all Ω ([34]).”
Absolute Continuity of Quasiconformal Mappings on Curves (2007, background): “Assume that there exists H ≥ 1 such that for each Bi = B(xi, ri) ∈ B we have that B ( f(xi), 12H diam(f(Bi)) ) ⊂ f(Bi) and B satisfies condition (ii) of Lemma 2.2.”
Intrinsic regular hypersurfaces in Heisenberg groups (2006, background): “First of all, we point out that the class of H-regular surfaces is deeply different from the class of Euclidean regular surfaces, in the sense that there are H -regular surfaces in ]HI 1 = R 3 that are (Euclidean) fractal sets (see [ 37 ]), and conversely there are continuously differentiable 2-subm”
Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs (2009, background): “A similar H-regular graph can be constructed in H with n 2, arguing as in [20].”
Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “We conclude this section by discussing the implications of Theorems 2.4 and 2.6 for the theory of horizontal rectifiability in codimension one in the setting of Carnot groups as developed by Franchi, Serapioni and Serra-Cassano, see e.g. [27],[26].”