Intrinsic regular hypersurfaces in Heisenberg groups

By Luigi Ambrosio, Francesco Serra Cassano, Davide Vittone. 2006

138 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a1a553c7dcaa41dab27e39bc6314a9548838dee

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In Applied Mathematics

In Geometry and Topology

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Citations in the corpus

The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations (2006, methodology): “ simply means topological codimension 1 surface. The notion of intrinsic graph has been recently introduced in [25] in the setting of a Carnot group and deeply studied in the case of hypersurfaces in [4] even if it was already implicitly exploited in [23]. The calibration method presented here is a ”
Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1 (2010, background): “Moreover the C 1 H smoothness of f implies that the function u is regular with respect to the projection on its domain of the vector fields in (1.1) (see [13] and [1]).”
Characterizations of intrinsic rectifiability in Heisenberg groups (2010, background): “A systematic study of H-regular surfaces has been recently carried out in [4, 5, 11, 17].”
Regularity of non-characteristic minimal graphs in the Heisenberg group $H^1$ (2008, background): “A deep result of Ambrosio, Serra-Cassano and Vittone [1] shows that such PDE continues to hold below the C2 threshold in a suitably weak sense.”
Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “It continues our program in this area [5, 4, 7], which is one component in a worldwide endeavor investigating sub-Riemannian geometric measure theory, including theories of rectifiability and perimeter [14], [26], [27], [17], [42], [3], [39]; fractals and tilings [56], [57]; geometric analysis of no”
On the Hausdorff volume in sub-Riemannian geometry (2010, background): “A deep study of Hausdorff measure for hypersurfaces in sub-Riemannian geometry, in particular in the context of Carnot groups, can be found in [8, 10, 11, 14, 19, 22, 32, 36] and references therein.”
Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, unknown): “so that dσH = √ 1 +Bφ(φ)2 dudv, see also [1].”
Geometry of Carnot-Caratheodory Spaces, Differentiability, Coarea and Area Formulas (2009, unknown): “Vittone [13], L.”
Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, background): “sano and Vittone [4] and Garofalo and Pauls [23] for vertical graphs. Additional contributions concerning variational problems related to the subriemannian area in the Heisenberg groups include [26], [2], [8], [9], [10], [21], [21], [20], [19], [18], [17], [16], [25], [29]. The recent monograph by C”