Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Vittone, Davide"'
We prove a Stepanov differentiability type theorem for intrinsic graphs in sub-Riemannian Heisenberg groups.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/2410.01526
We consider the following classical conjecture of Besicovitch: a $1$-dimensional Borel set in the plane with finite Hausdorff $1$-dimensional measure $\mathcal{H}^1$ which has lower density strictly larger than $\frac{1}{2}$ almost everywhere must be
Externí odkaz:
http://arxiv.org/abs/2404.17536
We introduce and study the notion of $C^1_\mathbb{H}$-regular submanifold with boundary in sub-Riemannian Heisenberg groups. As an application, we prove a version of Stokes' Theorem for $C^1_\mathbb{H}$-regular submanifolds with boundary that takes i
Externí odkaz:
http://arxiv.org/abs/2403.18675
We study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (depending only on the algebra of the group) on the codimension of the ab
Externí odkaz:
http://arxiv.org/abs/2203.16360
Publikováno v:
Systems & Control Letters, Volume 158, 2021
The evoluted set is the set of configurations reached from an initial set via a fixed flow for all times in a fixed interval. We find conditions on the initial set and on the flow ensuring that the evoluted set has negligible boundary (i.e. its Lebes
Externí odkaz:
http://arxiv.org/abs/2107.06739
We study the behavior of Lipschitz functions on intrinsic $C^1$ submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type approximation of Lipschit
Externí odkaz:
http://arxiv.org/abs/2107.00515
We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for
Externí odkaz:
http://arxiv.org/abs/2101.02985
Autor:
Vittone, Davide
Publikováno v:
Forum of Mathematics, Sigma 10 (2022) e6
The main result of the present paper is a Rademacher-type theorem for intrinsic Lipschitz graphs of codimension $k\leq n$ in sub-Riemannian Heisenberg groups $\mathbb H^n$. For the purpose of proving such a result we settle several related questions
Externí odkaz:
http://arxiv.org/abs/2007.14286
We consider submanifolds of sub-Riemannian Carnot groups with intrinsic $C^1$ regularity ($C^1_H$). Our first main result is an area formula for $C^1_H$ intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on recti
Externí odkaz:
http://arxiv.org/abs/2004.02520
In the setting of Carnot groups, we are concerned with the rectifiability problem for subsets that have finite sub-Riemannian perimeter. We introduce a new notion of rectifiability that is, possibly, weaker than the one introduced by Franchi, Serapio
Externí odkaz:
http://arxiv.org/abs/1912.00493