1,720,965 research outputs found
Convex hull property and exclosure theorems for H-minimal hypersurfaces in carnot groups
Full text linkIn 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 theorems” for H-minimal hypersurfaces of class C2 satisfying a
Hörmander-type condition
Hypersurfaces and variational formulas in sub-Riemannian Carnot groups
No full textAbstractIn 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 extensively used. Particular emphasis is given to the case of hypersurfaces. We state divergence-type theorems and integration by parts formulas with respect to the intrinsic measure σHn−1 on hypersurfaces. General formulas for the first and the second variation of the measure σHn−1 are proved
Some relations among volume, intrinsic perimeter and one-dimensional restrictions of functions in Carnot groups
Full text link[ARTICOLO
An integral formula on the Heisenberg group
Full text linkLet H^n denote the (2n+1)-dimensional (sub-Riemannian) Heisenberg group. In this note, we shall prove an integral identity (see Theorem 1.2) that generalizes a formula obtained in the Seventies by Reilly (Indiana Univ Math J 26(3):459–472, 1977). Some first applications will be given in Sect. 4
Stable H-Minimal Hypersurfaces
Full text linkWe prove some stability results for smooth non-characteristic
H-minimal hypersurfaces immersed in a sub-Riemannian k-step Carnot group
G. The main tools are the formulas for the first and second variation of the
H-perimeter measure together with some non-trivial geometric identities
Geometric inequalities in Carnot groups
No full textLet G 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
G, endowed with the H-perimeter measure
A note on the extension of BV functions in metric measure spaces
No full text[ARTICOLO] doi:10.1016/j.jmaa.2007.07.03
Regularity of the distance function to smooth hypersurfaces in some two-step carnot groups
Full text linkWe 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
Special functions: Euler's Gamma function and Riemann's Zeta function
Full text linkopenLa tesi tratta delle due funzioni Gamma di Eulero e Zeta di Riemann mettendo in evidenza le proprietà fondamentali e la connessione tra le due.This thesis deal with two fundamental function: Euler's Gamma function and Riemann' Zeta function. It develops some important properties of these function and their connection
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