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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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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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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Hilbert-Haar coordinates and Miranda's theorem in Lie groups
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of solutions to a class of quasilinear equations of non-degenerate p-Laplacian type on Lie groups that admit a system of Hilbert-Haar coordinates. These are coordinates with respect to which every linear function has zero
András Domokos, Juan J. Manfredi
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DFT screening of adsorption of biodiesel molecules on aluminum and stainless steel surfaces
Results in Surfaces and Interfaces, 2022 We present a Density Functional Theory (DFT) study of the adsorption of small organic molecules, taken as models of biodiesel autoxidation products, on stainless steel and aluminum surfaces.
Claudia Cantarelli +4 more
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A notion of rectifiability modeled on Carnot groups [PDF]
, 2004 We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N.
Pauls, Scott D.
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Nature and importance of follicular lymphoma precursors
Haematologica, 2014 It is now widely recognized that cancer development is a protracted process requiring the stepwise acquisition of multiple oncogenic events. In humans, this process can take decades, if not a lifetime, blurring the notion of ‘healthy’ individuals ...
Emilie Mamessier +6 more
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Sharp measure contraction property for generalized H-type Carnot groups [PDF]
, 2017 We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group.
Bonfiglioli A. +4 more
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On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations
Abstract and Applied Analysis, 2020 We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points.
Cecilia De Zan, Pierpaolo Soravia
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Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations [PDF]
, 2017 We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable.
Dirr, Nicolas +3 more
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