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Curvature exponent and geodesic dimension on Sard-regular Carnot groups [PDF]
Analysis and Geometry in Metric Spaces, 2023 In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
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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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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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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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Viscosity convex functions on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2003 We prove that any upper semicontinuous v-convex function in any Carnot group is h-convex.
Changyou Wang
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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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A notion of rectifiability modeled on Carnot groups [PDF]
Indiana University Mathematics Journal, 2000 27 ...
Scott D. Pauls
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Review of Carnot Battery Technology Commercial Development
Energies, 2022 Carnot batteries are a quickly developing group of technologies for medium and long duration electricity storage. It covers a large range of concepts which share processes of a conversion of power to heat, thermal energy storage (i.e., storing thermal ...
Vaclav Novotny +3 more
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Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics [PDF]
EntropyThe explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geometric ...
Frédéric Barbaresco
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