Surface measures in Carnot-Carathéodory spaces

By Roberto Monti, Francesco Serra Cassano. 2001

213 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d34a4b1103210a8fa86bebedc4f7ef6a0de862b1

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 Geometry and Topology

Citations in the corpus

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).”
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.”
A Notable Family of Entire Intrinsic Minimal Graphs in the Heisenberg Group which are not Perimeter Minimizing (2006, background): “defined as follows, see for instance [CDG], and [ GN ],”
Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group (2004, unknown): “This notion of intrinsically regular surface was introduced in order to study in the setting of Carnot groups, of which H1 is the simplest example, the classical problem in Geometric Measure Theory (GMT) of defining regular hypersurfaces (i.e. topological submanifold of codimension 1) and different…”
Examples of area-minimizing surfaces in the subriemannian Heisenberg group H^1 with low regularity (2008, background): “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].”
On gradient bounds for the heat kernel on the Heisenberg group (2007, methodology): “where � surfacet,x (∂A) is the perimeter of A for � t,x as defined in [1, Section 3] (see also [ 35 ]).”
Isoperimetric inequality in the Grushin plane (2004, background): “If E is a bounded open set with boundary of class C 2, then "lim inf" in (4.1) can be replaced by "lim" and the identity 9Y~a(OE) = P~(E) holds. This can be proved as in [ 17 ] Theorem 5.1.”
On the structure of finite perimeter sets in step 2 Carnot groups (2003, background): “dGf (xo)(v) = (VGf, 7rxo(V))xo �9 (2.15) For a proof see [ 55 ] Remark 3.3.”
Minimal Surfaces in the Heisenberg Group (2001, background): “The reader should also consult Z. Balough’s paper [Bal] concerning various aspect s of the perimeter measure for surfaces as well as a study of different surfaces measure in CC spaces by R. Monti and F. Serra Cassano ([ MSC99 ]).”