Results 11 to 20 of about 12,282,130 (266)
A Cornucopia of Carnot Groups in Low Dimensions
Analysis and Geometry in Metric Spaces, 2022 Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
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Measure contraction properties of Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2016 We prove that any corank 1 Carnot group of dimension $k+1$ equipped with a left-invariant measure satisfies the $\mathrm{MCP}(K,N)$ if and only if $K \leq 0$ and $N \geq k+3$.
Rizzi, Luca
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Geometric inequalities in Carnot groups [PDF]
Pacific Journal of Mathematics, 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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Analysis and Geometry in Metric Spaces, 2018 Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance.
Le Donne Enrico
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Isodiametric inequality in Carnot groups
Annales Academiae Scientiarum Fennicae Mathematica, 2010 The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups.
Rigot, Severine
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A sufficient condition for nonrigidity of Carnot groups [PDF]
Mathematische Zeitschrift, 2018 In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group.
Ottazzi, Alessandro
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A note on lifting of Carnot groups
Revista Matemática Iberoamericana, 2005 We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
Andrea Bonfiglioli, Francesco Uguzzoni
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On rectifiable measures in Carnot groups: representation [PDF]
Calculus of Variations and Partial Differential Equations, 2021 AbstractThis paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in ...
Gioacchino Antonelli, Andrea Merlo
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Attainable Set for Rank 3 Step 2 Free Carnot Group with Positive Controls [PDF]
2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2022 We find the attainable set for a control system on the free Carnot group of rank 3 and step 2 with positive controls. This kind of control systems is connected with the theory of free Lie semigroups; with some estimates for probabilities of inequalities ...
A. Podobryaev
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Rearrangements in Carnot Groups [PDF]
Acta Mathematica Sinica, English Series, 2018 In this paper we extend the notion of rearrangement of nonnegative functions to the setting of Carnot groups. We define rearrangement with respect to a given family of anisotropic balls B_r or equivalently with respect to a gauge |x|, and prove basic regularity properties of this construction.
Juan J. Manfredi +1 more
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