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We characterize smooth maps between sub-Riemannian Lie groups that commute with sub-Laplacians. We show they are sub-Riemannian conformal submersions. Our work clarifies the analysis initiated on Carnot groups in \cite{MR2363343}. In particular, we s
Externí odkaz:
http://arxiv.org/abs/2501.00576
We prove that the uniform doubling property holds for every Lie group which can be written as a quotient group of $\operatorname{SU}(2) \times \mathbb{R}^n$ for some $n$. In particular, this class includes the four-dimensional unitary group $\operato
Externí odkaz:
http://arxiv.org/abs/2412.17102
One way to define a sub-Riemannian metric is as the limit of a Riemannian metric. Consider a Riemannian structure depending on a parameter $s$ such that its limit defines a sub-Riemannian metric when $s \to \infty$, assuming that the Riemannian geode
Externí odkaz:
http://arxiv.org/abs/2411.09008
Autor:
Dietze, Charlotte, Read, Larry
We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter regime, we id
Externí odkaz:
http://arxiv.org/abs/2410.20563
From the classical theory of Lie algebras, it is well-known that the bilinear form $B(X,Y)={\rm tr}(XY)$ defines a non-degenerate scalar product on the simple Lie algebra ${\mathfrak{sl}}(n,{\mathbb R})$. Diagonalizing the Gram matrix $Gr$ associated
Externí odkaz:
http://arxiv.org/abs/2410.15478
Autor:
Donne, Enrico Le
This book explores geometries defined by left-invariant distance functions on Lie groups, with a particular focus on nilpotent groups and Carnot groups equipped with geodesic distances. Geodesic left-invariant metrics are either sub-Riemannian or the
Externí odkaz:
http://arxiv.org/abs/2410.07291
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:
Grochowski, Marek
In the present paper we deal with (local) infinitesimal isometries of special sub-Riemannian manifolds (a contact and oriented sub-Riemannian manifold is called special if the Reeb vector field is an isometry). The objective of the paper is to find s
Externí odkaz:
http://arxiv.org/abs/2410.00786
In this paper we solve the Bernstein problem for a broad class of smooth, non-characteristic hypersurfaces in the second sub-Riemannian Heisenberg group $\mathbb{H}^2$.
Externí odkaz:
http://arxiv.org/abs/2409.20359
A definable choice is a semialgebraic selection of one point in every fiber of the projection of a semialgebraic set. Definable choices exist by semialgebraic triviality, but their complexity depends exponentially on the number of variables. By allow
Externí odkaz:
http://arxiv.org/abs/2409.14869