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Documents  Sigalotti, Mario | enregistrements trouvés : 6

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Research talks;Geometry

A sub-Riemannian distance is obtained when minimizing lengths of paths which are tangent to a distribution of planes. Such distances differ substantially from Riemannian distances, even in the simplest example, the 3-dimensional Heisenberg group. This raises many questions in metric geometry: embeddability in Banach spaces, bi-Lipschitz or bi-Hölder comparison of various examples. Emphasis will be put on Gromov's results on the Hölder homeomorphism problem, and on a quasisymmetric version of it motivated by Riemannian geometry. A sub-Riemannian distance is obtained when minimizing lengths of paths which are tangent to a distribution of planes. Such distances differ substantially from Riemannian distances, even in the simplest example, the 3-dimensional Heisenberg group. This raises many questions in metric geometry: embeddability in Banach spaces, bi-Lipschitz or bi-Hölder comparison of various examples. Emphasis will be put on Gromov's results on the Hölder ...

53C20 ; 53C15

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Research talks;Algebraic and Complex Geometry

In this course, we will define the sub-Laplacian associated with a sub-Riemannian structure, and we will describe its hypoellipticity under the Hormander condition. We will introduce the main tools for the study of sub-elliptic PDEs.

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Research talks;Probability and Statistics

We discuss hypoelliptic and subelliptic diffusions; the lectures include the following topics: Malliavin calculus; Hormander's theorem; smoothness of transition probabilities under Hormander's brackets condition; control theory and Stroock-Varadhan's support theorems; hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semi-groups; notions of curvature related to sub-Riemannian diffusions. We discuss hypoelliptic and subelliptic diffusions; the lectures include the following topics: Malliavin calculus; Hormander's theorem; smoothness of transition probabilities under Hormander's brackets condition; control theory and Stroock-Varadhan's support theorems; hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semi-groups; notions of curvature related to sub-Riemannian ...

60H07 ; 60J60 ; 58J65

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Research talks;Control Theory and Optimization;Geometry

This will be an introduction to sub-Riemannian geometry from the point of view of control theory. We will define sub-Riemannian structures and prove the Chow Theorem. We will describe normal and abnormal geodesics and discuss the completeness of the Carnot-Carathéodory distance (Hopf-Rinow Theorem). Several examples will be given (Heisenberg group, Martinet distribution, Grusin plane).

53C17 ; 49Jxx

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- vi; 324 p.
ISBN 978-3-03719-162-0

EMS series of lectures in mathematics

Localisation : Ouvrage RdC (GEOM)

géométrie sous-Riemanienne # opérateur hypoelliptique # contrainte non-holonome # contrôle optimal # chemin rugueux

53C17 ; 35H10 ; 60H30 ; 49J15 ; 53-06 ; 00B15

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- viii; 299 p.
ISBN 978-3-03719-163-7

EMS series of lectures in mathematics

Localisation : Ouvrage RdC (GEOM)

géométrie sous-Riemanienne # opérateur hypoelliptique # contrainte non-holonome # contrôle optimal # chemin rugueux

53C17 ; 35H10 ; 60H30 ; 49J15 ; 53-06 ; 00B15

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