Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Rigot, Séverine"'
Autor:
Rigot, Séverine
Monotone sets have been introduced about ten years ago by Cheeger and Kleiner who reduced the proof of the non biLipschitz embeddability of the Heisenberg group into $L^1$ to the classification of its monotone subsets. Later on, monotone sets played
Externí odkaz:
http://arxiv.org/abs/2206.03094
Autor:
Morbidelli, Daniele, Rigot, Séverine
A subset of a Carnot group is said to be precisely monotone if the restriction of its characteristic function to each integral curve of every left-invariant horizontal vector field is monotone. Equivalently, a precisely monotone set is a h-convex set
Externí odkaz:
http://arxiv.org/abs/2106.13490
In this paper we introduce the notion of horizontally affine, h-affine in short, function and give a complete description of such functions on step-2 Carnot algebras. We show that the vector space of h-affine functions on the free step-2 rank-$n$ Car
Externí odkaz:
http://arxiv.org/abs/2004.08129
Autor:
Rigot, Séverine
Several quantitative notions of rectifiability in the Heisenberg groups have emerged in the recent literature. In this paper we study the relationship between two of them, the big pieces of intrinsic Lipschitz graphs (BPiLG) condition and the bilater
Externí odkaz:
http://arxiv.org/abs/1904.06904
A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$
Externí odkaz:
http://arxiv.org/abs/1803.04819
Autor:
Golo, Sebastiano, Rigot, Séverine
The Besicovitch covering property (BCP) is known to be one of the fundamental tools in measure theory, and more generally, a usefull property for numerous purposes in analysis and geometry. We prove both sufficient and necessary criteria for the vali
Externí odkaz:
http://arxiv.org/abs/1803.04502
Autor:
Rigot, Severine
The theory of differentiation of measures originates from works of Besicovitch in the 1940's. His pioneering works, as well as subsequent developments of the theory, rely as fundamental tools on suitable covering properties. The first aim of these no
Externí odkaz:
http://arxiv.org/abs/1802.02069
Autor:
Donne, Enrico Le, Rigot, Severine
We give a complete answer to which homogeneous groups admit homogeneous distances for which the Besicovitch Covering Property (BCP) holds. In particular, we prove that a stratified group admits homogeneous distances for which BCP holds if and only if
Externí odkaz:
http://arxiv.org/abs/1512.04936
Autor:
Donne, Enrico Le, Rigot, Severine
We prove that the Besicovitch Covering Property (BCP) does not hold for some classes of homogeneous quasi-distances on Carnot groups of step 3 and higher. As a special case we get that, in Carnot groups of step 3 and higher, BCP is not satisfied for
Externí odkaz:
http://arxiv.org/abs/1503.09034
Autor:
Donne, Enrico Le, Rigot, Severine
Our main result is a positive answer to the question whether one can find homogeneous distances on the Heisenberg groups that have the Besicovitch Covering Property (BCP). This property is well known to be one of the fundamental tools of measure theo
Externí odkaz:
http://arxiv.org/abs/1406.1484