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Starshapedness and convexity in carnot groups and geometry of hormander vector fields

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Publicado en:PQDT - UK & Ireland (2018)
Autor principal: Filali, Doaa
Publicado:
ProQuest Dissertations & Theses
Materias:
Euclidean space
Acceso en línea:Citation/Abstract
Full text outside of ProQuest
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100 1 |a Filali, Doaa 
245 1 |a Starshapedness and convexity in carnot groups and geometry of hormander vector fields 
260 |b ProQuest Dissertations & Theses  |c 2018 
513 |a Dissertation/Thesis 
520 3 |a Sub-Riemannian geometries are very important, not only for a pure mathe-matics point of view but also for the many applications in physics (see [73]), in economics (see e.g [76]), in biology and image processing (for example visual vertex model by Citti-Sarti [33]). Sub-Riemannian geometries are manifolds where the Riemannian metric is de-fined only on subbundle of the tangent bundle, and this leads to constrains on the allowed directions when moving on the manifold. In particular, we look at the case when the distribution generating the subbundle satisfies the bracket generating condition (see Definition 2.1.1). This implies that, even if some directions are forbidden, we can still move everywhere on the manifold. Un-like the Riemannian case, these geometries are not equivalent to the Euclidean space at any scaling, and presents substantial differences w.r.t. more known Riemannian case (see Section 2.2). 
653 |a Euclidean space 
773 0 |t PQDT - UK & Ireland  |g (2018) 
786 0 |d ProQuest  |t ProQuest Dissertations & Theses Global 
856 4 1 |3 Citation/Abstract  |u https://www.proquest.com/docview/2204707287/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch 
856 4 0 |3 Full text outside of ProQuest  |u http://orca.cf.ac.uk/117459/