7 citations · 23 across the 9 of their papers we have counts for
10 papers
The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups
Annalisa Baldi, Francescopaolo Montefalcone
We define a BV -type space in the setting of Carnot groups (i.e., simply connected Lie groups with stratified nilpotent Lie algebra) that allows one to characterize all distributio…
CMC spheres in the Heisenberg group
Valentina Franceschi, Francescopaolo Montefalcone, Roberto Monti
We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group . These spheres are conjectured to be the isoperimetric sets of . We pr…
An integral formula on the Heisenberg group
Francescopaolo Montefalcone
Let Hn denote the (2n + 1)-dimensional (sub-Riemannian) Heisenberg group. In this note, we shall prove an integral identity (see Theorem 1.2) which generalizes a formula obtained i…
Geometric inequalities in Carnot groups
Francescopaolo Montefalcone
Let $\GG$ be a sub-Riemannian -step Carnot group of homogeneous dimension . In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e.…
Stable H-minimal hypersurfaces
Francescopaolo Montefalcone
We prove some stability results for smooth H-minimal hypersurfaces immersed in a sub-Riemannian k-step Carnot group G. The main tools are the formulas for the 1st and 2nd variation…
Stability of Heisenberg Isoperimetric Profiles
Francescopaolo Montefalcone
In the context of sub-Riemannian Heisenberg groups Hn, n \geq 1, we shall study Isoperimetric Profiles, which are closed compact hypersurfaces having constant horizontal mean curva…
Hypergeometric solutions of the closed eigenvalue problem on Heisenberg Isoperimetric Profiles
Francescopaolo Montefalcone
After introducing the sub-Riemannian geometry of the Heisenberg group Hn, n \geq 1, we recall some basics about hypersurfaces endowed with the H-perimeter measure and horizontal Gr…
Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Francescopaolo Montefalcone
Let G be a k-step Carnot group. We prove an isoperimetric-type inequality for compact C^2-smooth immersed hypersurfaces with boundary, involving the horizontal mean curvature of th…
Isoperimetric, Sobolev and Poincaré inequalities on hypersurfaces in sub-Riemannian Carnot groups
F. Montefalcone
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Among other results, we shall prove an isoperimetric inequality for…
CC-distance and metric normal of smooth hypersurfaces in sub-Riemannian Carnot groups
N. Arcozzi, F. Ferrari, F. Montefalcone
In this paper we study the main geometric properties of the Carnot-Carathéodory (abbreviated CC) distance $\dc$ in the setting of -step sub-Riemannian Carnot groups from many di…