Rectifiability and perimeter in the Heisenberg group

By Bruno Franchi, Raul Paolo Serapioni, Francesco Serra Cassano. 2001

411 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/bb8d1b38c39cc84bf8bf4abb7b4a53ed40c53a44

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Minimal Surfaces in the Heisenberg Group (2001, result): “We state thi s result (a version of results in [ FSSC96 ] and [GN96]) for the convenience of the reader:”
Surface measures in Carnot-Carathéodory spaces (2001, background): “This coarea formula extends previous ones already known in the literature (see [27], [30] and [ 29 ]).”
Convex isoperimetric sets in the Heisenberg group (2006, methodology): “of class C2), perimeter coincides with the Minkowski content and with the 3-dimensional Hausdorff measure of ∂ E constructed by means of the standard Carnot-Carathéodory metric in H1 (see [16] and [9], respectively).”
Minimal surfaces in pseudohermitian geometry (2004, neutral): “The p-area can also be identified with the 3-dimensional spherical Hausdor measure of (see, e.g., [B], [ FSS ]).”
Regular submanifolds, graphs and area formula in Heisenberg groups (2007, neutral): “Appendix: Federer-Fleming Currents 42 References 47”
Existence and uniqueness for P-area minimizers in the Heisenberg group (2006, background): “The p-minimal (or X-minimal, H-minimal in the terminology of some authors, e.g., [ 6 ], [7], [16]) surfaces have been studied extensively in the framework of geometric measure theory.”
Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group H1 (2006, background): “A closely related remarkable fact, discovered in [ FSS1 ], is that the blow-up `a la De Giorgi of a set with locally finite H-perimeter at a point of its reduced boundary is again a plane such as (1.2).”
H-minimal graphs of low regularity in H1 (2006, methodology): “While this theorem recovers the characterization of such H-minimal surfaces as unions of ruled surfaces in the Heisenberg group, it still leaves a gap between the baseline results of Franchi, Serra Cassano and Serapioni and theorem 1.1.”
TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS (2007, background): “Serapioni and Serra Cassano, [ 19 ], [20] in the case M = R and more recently in Heisenberg groups with M = Rk, [22].”
IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES (2006, background): “The proof of the existence of the implicit function is similar to the one in [12], but technically, much simpler.”
Characterizations of intrinsic rectifiability in Heisenberg groups (2010, methodology): “2; this tangent measure is always supported on THS(p), hence it is supported on a subgroup in G(Hn) (see [14, 16, 26]).”
Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups (2011, background): “17, the subgraph of fi has locally finite H-perimeter and, eventually, it is (2n,H)-rectifiable, by the structure theorem for sets of locally finite H-perimeter proved in [17].”
On the structure of finite perimeter sets in step 2 Carnot groups (2003, methodology): “Results strictly related to ours are quoted in the body of the article and here we restrict ourselves to recommend the reader to the general monographies [ 18, 43, 42, 41,64, 66, 53], to the articles [4, 5, 6, 12, 15, 16, 29, 32 , 37, 47, 57, 56, 67] and to the references therein.”