Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Montefalcone, Francescopaolo"'
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 distributions F for which there exists a continuous horizontal vector field {\Phi
Externí odkaz:
http://arxiv.org/abs/2210.15490
We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group $H^1$. These spheres are conjectured to be the isoperimetric sets of $H^1$. We prove several results supporting this conjecture. We also focus our atte
Externí odkaz:
http://arxiv.org/abs/1611.09215
Autor:
Montefalcone, Francescopaolo
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 in the Seventies by Reilly. Some first applications will be given in Se
Externí odkaz:
http://arxiv.org/abs/1203.5975
Autor:
Montefalcone, Francescopaolo
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 of the H-perimeter measure.
Comment: 34 pages
Comment: 34 pages
Externí odkaz:
http://arxiv.org/abs/1203.5972
Autor:
Montefalcone, Francescopaolo
Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e. codimension one submanifolds) immersed in $\GG$, endowed with the $\H
Externí odkaz:
http://arxiv.org/abs/1203.5973
Autor:
Montefalcone, Francescopaolo
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 Green's formulas. Then, we describe a class of compact closed hypersurfa
Externí odkaz:
http://arxiv.org/abs/1110.0703
Autor:
Montefalcone, Francescopaolo
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 curvature, very similar to ellipsoids. Our main goal is to study the stabil
Externí odkaz:
http://arxiv.org/abs/1110.0707
Autor:
Montefalcone, Francescopaolo
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 the hypersurface. This generalizes an inequality due to Michael and Simo
Externí odkaz:
http://arxiv.org/abs/1012.2442
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 7, Iss 1, Pp 109-129 (2019)
We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture. We also focus our attention
Externí odkaz:
https://doaj.org/article/d40d427797114dd6b32bd009ea946e1e
Autor:
Montefalcone Francescopaolo
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 4, Iss 1 (2016)
In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups. In this case, we will prove the convex hull property and some “exclosure theor
Externí odkaz:
https://doaj.org/article/83a795f317304c76bad5e16c0e1a0786