Results 31 to 40 of about 12,576,498 (281)
Analysis and Geometry in Metric Spaces, 2014 A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups.
Franchi Bruno +2 more
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Structure of porous sets in Carnot groups [PDF]
Illinois Journal of Mathematics, 2017 23 ...
Pinamonti A., Speight G.
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Conformality and Q-harmonicity in Carnot groups
Duke Mathematical Journal, 2006 The main theorem of this paper is that 1-quasiconformal maps are smooth in all Carnot groups. This theorem can be used to prove rigidity theorems for quasiconformal maps between open subsets in certain classes of groups without any a priori smoothness assumption.
Capogna, Luca, Cowling, Michael
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Geometric inequalities in Carnot groups [PDF]
, 2012 Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e.
Montefalcone, Francescopaolo
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Identifying 1-rectifiable measures in Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R.
Badger Matthew, Li Sean, Zimmerman Scott
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Quasiconformal maps on a 2-step Carnot group
, 2019 We find all global quasiconformal maps (with respect to the Carnot metric) on a particular 2-step Carnot group.
Christopher J. Gardiner
semanticscholar +1 more source
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
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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
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On the Lie Algebra of polarizable Carnot groups [PDF]
Analysis and Mathematical Physics, 2020 Let \(G\) be a Carnot group equipped with a left-invariant sub-Riemannian metric, induced by an inner product \(\langle \cdot, \cdot \rangle\) on the first layer of its Lie algebra \(\mathfrak{g}\). The metric induces a family of \(p\)-sub-Laplacians \(\Delta_p\) on \(G\), where \(\Delta_2\) is the usual sub-Laplacian. Following [\textit{Z. M.
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Harnessing Colloidal Dispersion for Laccase‐Driven Enzymatic Depolymerization of Polystyrene
Angewandte Chemie, EarlyView.Polystyrene (PS), long considered non‐degradable by biocatalytic pathways, can now be broken down under aqueous conditions using atmospheric air and a laccase–mediator system composed of a commercially available fungal enzyme and 1‐hydroxybenzotriazole as small organic mediator.
Manon Pujol +5 more
wiley +2 more sources