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Dimension Phenomena and Curvature Equations in Carnot Groups

The core of this project can be shortly (and roughly) described as project in Geometric Metric Theory and curvature equations in non-Euclidean structures. It is worthwhile from the very beginning to state clearly that, when we men... ver más

28/02/2013

UNIBO

65K€

Presupuesto del proyecto: 65K€

Líder del proyecto

ALMA MATER STUDIORUM UNIVERSITA DI BOLOGNA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

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Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2013-02-28 No tenemos la información de la convocatoria

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3 Participantes

UNIBO

0.00€ | Lider

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UNIVERSITAET BERN

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Líder del proyecto

ALMA MATER STUDIORUM UNIVERSITA DI BOLOGNA No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 65K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The core of this project can be shortly (and roughly) described as project in Geometric Metric Theory and curvature equations in non-Euclidean structures. It is worthwhile from the very beginning to state clearly that, when we mention non-Euclidean structures, we refer to metric structures that are not Euclidean at any scale. Thus, the model we have in mind are not Riemannian manifolds, but better the so-called sub-Riemannian manifolds and fractals, or even fractals in sub-Riemannian spaces. In the last few years, sub-Riemannian structures have been largely studied in several respects, such as differential geometry, geometric measure theory, subelliptic differential equations, complex variables, optimal control theory, mathematical models in neurosciences, non-holonomic mechanics, robotics. Among all sub-Riemannian structures, a prominent position is taken by the so-called Carnot groups (simply connected Lie groups G with stratified nilpotent algebra), which play versus sub Riemannian spaces the role played by Euclidean spaces (considered as tangent spaces) versus Riemannian manifolds. The notion of dimension is crucial in our approach: the non-Euclidean character of the structures we are interested to study hides in the gap between the topological dimension of a group G and its metric dimension. Isoperimetric inequalities, analysis on fractal sets, quasiconformal and quasiregular maps are a typical manifestations of the metric dimension versus the topological dimension. In addition, dimension phenomena appear in a crucial way when dealing with intrinsic curvature in submanifolds of Carnot groups and in the curvature equations.

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