Zobrazeno 1 - 10
of 4 807
pro vyhledávání: '"Heisenberg groups"'
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
Autor:
Adamowicz, Tomasz, Gryszówka, Marcin
We study the Carleson measures on NTA and ADP domains in the Heisenberg groups $\mathbb{H}^n$ and provide two characterizations of such measures: (1) in terms of the level sets of subelliptic harmonic functions and (2) via the $1$-quasiconformal fami
Externí odkaz:
http://arxiv.org/abs/2409.01096
The purpose of the paper is threefold: first, we prove optimal regularity results for the distance from $C^k$ submanifolds of general rank-varying sub-Riemannian structures. Then, we study the asymptotics of the volume of tubular neighbourhoods aroun
Externí odkaz:
http://arxiv.org/abs/2408.16838
Autor:
Deloup, Florian L.
It is known that an abelian group $A$ and a $2$-cocycle $c:A \times A \to C$ yield a group ${\mathscr{H}}(A,C,c)$ which we call a Heisenberg group. This group, a central extension of $A$, is the archetype of a class~$2$ nilpotent group. In this note,
Externí odkaz:
http://arxiv.org/abs/2409.03399
The curvature exponent $N_{\mathrm{curv}}$ of a metric measure space is the smallest number $N$ for which the measure contraction property $\mathsf{MCP}(0,N)$ holds. In this paper, we study the curvature exponent of sub-Finsler Heisenberg groups equi
Externí odkaz:
http://arxiv.org/abs/2407.14619
Autor:
Pozuelo, Julián, Verzellesi, Simone
We study the prescribed mean curvature equation for $t$-graphs in a Riemannian Heisenberg group of arbitrary dimension. We characterize the existence of classical solutions in a bounded domain without imposing Dirichlet boundary data, and we provide
Externí odkaz:
http://arxiv.org/abs/2405.06533
Autor:
Shafrir, Doron
If $G$ is a nilpotent group and $[G,G]$ has Hirsch length $1$, then every f.g. submonoid of $G$ is boundedly generated, i.e. a product of cyclic submonoids. Using a reduction of Bodart, this implies the decidability of the submonoid membership proble
Externí odkaz:
http://arxiv.org/abs/2405.05939
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