Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Francescopaolo Montefalcone"'
Publikováno v:
Bruno Pini Mathematical Analysis Seminar, Vol 14, Iss 2, Pp 42-55 (2024)
In the setting of Carnot groups (connected, simply connected and stratified Lie groups), we prove a density result for a BV-type space previously introduced in [3]. In addition, we relate the dual of this BV-type space with the dual of the well known
Externí odkaz:
https://doaj.org/article/b7d82bb736594ef3815b74d9ff3e19e5
In this paper, we will prove several generalized versions, dependent on different boundary conditions, of the classical Gaffney–Friedrichs inequality for differential forms on Heisenberg groups. In the first part of the paper, we will consider hori
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e0fe1da4a37088122eb6740b293ec0ad
http://hdl.handle.net/11585/711415
http://hdl.handle.net/11585/711415
We study geometric properties of the Carnot-Carathéodory signed distance δs to a smooth hypersurface S in some 2-step Carnot groups. In particular, a sub-Riemannian version of Gauss' Lemma is proved.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e849a27a4843bf763581124c4aab09d
http://hdl.handle.net/11585/586681
http://hdl.handle.net/11585/586681
Autor:
Francescopaolo Montefalcone
Publikováno v:
The Journal of Geometric Analysis. 25:820-870
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c595f2ea900adbbab7d86c92fd793d44
https://doi.org/10.1007/s12220-013-9447-0
https://doi.org/10.1007/s12220-013-9447-0
Autor:
Francescopaolo Montefalcone
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://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c34cf3d641a89007339c16ff06fccfc
http://hdl.handle.net/11577/3228821
http://hdl.handle.net/11577/3228821
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 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 attentio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c8a1a35e9800dd2762806d28cf57569
Autor:
Francescopaolo Montefalcone
Publikováno v:
Annali di Matematica Pura ed Applicata. 193:405-422
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad84c944dd4f0bae42777edd40c5897b
https://doi.org/10.1007/s10231-012-0282-x
https://doi.org/10.1007/s10231-012-0282-x
Autor:
Francescopaolo Montefalcone
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b2c3a0cbc677616bdaa7df9230b5131
http://arxiv.org/abs/1203.5973
http://arxiv.org/abs/1203.5973
In this note, a classical extension result for BV functions due to Yu.D. Burago and V.G. Maz'ja [Yu.D. Burago, V.G. Maz'ja, Potential Theory and Function Theory for Irregular Regions, Seminars in Math., vol. 3, V.A. Steklov Math. Inst., Leningrad, 19
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::897cbd18cebeebf3058180e61c5d6f2f
http://hdl.handle.net/11577/157468
http://hdl.handle.net/11577/157468
Autor:
Francescopaolo Montefalcone
In this paper we study smooth immersed non-characteristic submanifolds (with or without boundary) of k-step sub-Riemannian Carnot groups, from a differential-geometric point of view. The methods of exterior differential forms and moving frames are ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8419337bf452970c7bd11c70721c9d40
http://hdl.handle.net/11577/157469
http://hdl.handle.net/11577/157469