Results 71 to 80 of about 12,319,056 (272)
On criticality coupled sub-Laplacian systems with Hardy type potentials on Stratified Lie groups
Communications in Analysis and Mechanics, 2023 In this work, our main concern is to study the existence and multiplicity of solutions for the following sub-elliptic system with Hardy type potentials and multiple critical exponents on Carnot group $ \begin{equation*} \left\{\begin{aligned} & ...
Jinguo Zhang , Shuhai Zhu
doaj +1 more source
The Traveling Salesman Theorem in Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2018 Let $\mathbb{G}$ be any Carnot group. We prove that, if a subset of $\mathbb{G}$ is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natural modifications. We thus prove one direction of the Traveling Salesman Theorem in $\mathbb{G}$.
Sean Li +2 more
openaire +3 more sources
Space of signatures as inverse limits of Carnot groups [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2021 We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by ...
Roger Züst +2 more
openaire +4 more sources
Morrey-Campanato Functional Spaces for Carnot Groups [PDF]
arXiv, 2023 We shortly review the historical path of Morrey-Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey-Campanato spaces in the framework of Carnot groups.
arxiv
BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Analysis and Geometry in Metric Spaces, 2015 Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
doaj +1 more source
Metric spaces with unique tangents [PDF]
, 2010 We are interested in studying doubling metric spaces with the property that at some of the points the metric tangent is unique. In such a setting, Finsler-Carnot-Caratheodory geometries and Carnot groups appear as models for the tangents. The results are
Donne, Enrico Le
core +2 more sources
Intrinsic regular surfaces in Carnot groups
Bruno Pini Mathematical Analysis SeminarA Carnot group $G$ is a simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C1 surfaces in Euclidean spaces.
Daniela Di Donato
doaj +1 more source
Invertible Carnot Groups [PDF]
, 2016 We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman, David M.
core
Angewandte Chemie International Edition, Accepted Article.We herein introduce a method for the direct a‐amination of different carbonyl compounds by employing aqueous ammonia as the N‐source. Upon using NH3 in combination with hypochlorites as simple oxidants under phase‐transfer catalytic conditions it is possible to carry out the direct a‐amination of reactive enolate‐precursors such as cyclic b‐ketoesters,
Christopher Mairhofer +6 more
wiley +1 more source
A Comprehensive Review of Intramolecular Hydrosilylation of Alkynes and Alkenes
ChemCatChem, Accepted Article.Hydrosilylation reactions of alkenes and alkynes have been widely used to form compounds containing a silicon atom. Applied in intramolecular version, these processes enable the formation of silylated heterocycles, which are important building blocks in the synthesis of drugs, fragrances or materials.
Mathias Reboli, Muriel Durandetti
wiley +1 more source