Results 71 to 80 of about 12,576,498 (281)

Lipschitz and bilipschitz maps on Carnot groups [PDF]

Pacific Journal of Mathematics, 2013
Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of A of positive Hausdorff measure.
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A proof of Hörmander’s theorem for sublaplacians on Carnot groups [PDF]

Nonlinear Analysis, 2015
Let \(G\) be a Carnot group and let \(\mathcal{L}\) be its left-invariant sub-Laplacian. As a consequence of Hörmander's theorem, \(\mathcal{L}\) is hypoelliptic, that is, for every distribution \(u\) on \(G\), if \(\mathcal{L}u \in C^\infty\), then \(u \in C^\infty\).
Bramanti, Marco, Brandolini, Luca
openaire   +1 more source

Nonlinear Pulse Shaping in Fibres for Pulse Generation and Optical Processing

International Journal of Optics, 2012
The development of new all-optical technologies for data processing and signal manipulation is a field of growing importance with a strong potential for numerous applications in diverse areas of modern science.
Sonia Boscolo, Christophe Finot
doaj   +1 more source

Almost uniform domains and Poincaré inequalities

Transactions of the London Mathematical Society, 2021
Here we show existence of many subsets of Euclidean spaces that, despite having empty interior, still support Poincaré inequalities with respect to the restricted Lebesgue measure.
Sylvester Eriksson‐Bique, Jasun Gong
doaj   +1 more source

Loomis–Whitney inequalities on corank 1 Carnot groups [PDF]

Annales Fennici Mathematici
In this paper we provide another way to deduce the Loomis–Whitney inequality on higher dimensional Heisenberg groups \(\mathbb{H}^n\) based on the one on the first Heisenberg group \(\mathbb{H}^1\) and the known nonlinear Loomis–Whitney inequality (which
Ye Zhang
semanticscholar   +1 more source

A sufficient condition for nonrigidity of Carnot groups [PDF]

, 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
core  

Porosity, Differentiability and Pansu's Theorem

, 2016
We use porosity to study differentiability of Lipschitz maps on Carnot groups. Our first result states that directional derivatives of a Lipschitz function act linearly outside a $\sigma$-porous set.
Pinamonti, Andrea, Speight, Gareth
core   +1 more source

Future Perspective On Materials, Electrochemistry, and Cell Concepts for Redox‐Mediated CO2 Direct Air Capture Scenarios

ChemistryEurope, EarlyView.
Direct air capture (DAC) of carbon dioxide (CO2) emerges as a key strategy for climate crisis mitigation. Redox‐mediated electrochemical carbon capture offers a promising route for energy‐efficient DAC. This perspective discusses recent advances in the field, highlighting key challenges, such as oxygen interference at low CO2 concentrations, and ...
Tilmann J. Neubert, Martin Oschatz
wiley   +1 more source

APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS [PDF]

Communications in Contemporary Mathematics, 2011
This paper deals with a notion of Sobolev space W1, pintroduced by Bourgain, Brezis and Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by Ponce to obtain a Poincaré-type inequality.
openaire   +3 more sources

Minimal surfaces in the Heisenberg group

, 2006
We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial ...
Pauls, Scott D.
core   +1 more source