Regular submanifolds, graphs and area formula in Heisenberg groups

By Bruno Franchi, Raul Paolo Serapioni, Francesco Serra Cassano. 2007

145 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d0d256acd0cdd7e21bf992fe79f2ca8130c227af

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Intrinsic regular hypersurfaces in Heisenberg groups (2006, background): “The two key points we want to stress now are the notions of intrinsic regular hypersurface and graph in H n. A general and more complete discussion of these topics in Carnot groups can be found in [ 30 ].”
Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs (2009, methodology): “A general and more complete discussion of these topics in Carnot groups can be found in [18].”
Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups (2011, background): “To motivate the centrality of intrinsic differentiable functions we recall the following theorem that is the main result in [4], (see also [19]).”
TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS (2007, methodology): “This is indeed the case for (Hn, Rk)-regular sets of Hn, with 1 ≤ k ≤ n, for which Franchi, Serapioni and Serra Cassano have also established an area-type formula to compute their spherical Hausdorff measure [7].”
The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations (2006, methodology): “1”
Characteristic points, rectifiability and perimeter measure on stratified groups (2006, methodology): “Presently, this question has been positively answered for k = 1 and arbitrary G in [28] and for k n and G = H in [30].”
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”