Grégoire Charlot
Lipschitz classification of almost-Riemannian distances on compact oriented surfaces.
Fri, 03/26/2010 - 16:01 — SomNambulAuthors: Ugo Boscain, Grégoire Charlot, Roberta Ghezzi, Mario Sigalotti
Subjects: Optimization and Control
AbstractTwo-dimensional almost-Riemannian structures are generalized Riemannian
structures on surfaces for which a local orthonormal frame is given by a Lie
bracket generating pair of vector fields that can become collinear. We consider
the Carnot--Caratheodory distance canonically associated with an
almost-Riemannian structure and study the problem of Lipschitz equivalence
between two such distances on the same compact oriented surface.Existence of planar curves minimizing length and curvature.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Ugo Boscain, Grégoire Charlot, Francesco Rossi
Subjects: Differential Geometry
AbstractIn this paper we consider the problem of reconstructing a curve that is
partially hidden or corrupted by minimizing the functional $\int
\sqrt{1+K_\gamma^2} ds$, depending both on length and curvature $K$. We fix
starting and ending points as well as initial and final directions.For this functional we discuss the problem of existence of minimizers on
various functional spaces. We find non-existence of minimizers in cases in
which initial and final directions are considered with orientation. In this
case, minimizing sequences of trajectories can converge to curves with angles.Two-Dimensional Almost-Riemannian Structures with Tangency Points.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: Andrei Agrachev, Ugo Boscain, Grégoire Charlot, Roberta Ghezzi, Mario Sigalotti
Subjects: Differential Geometry
AbstractTwo-dimensional almost-Riemannian structures are generalized Riemannian
structures on surfaces for which a local orthonormal frame is given by a Lie
bracket generating pair of vector ?elds that can become collinear. We study the
relation between the topological invariants of an almost-Riemannian structure
on a compact oriented surface and the rank-two vector bundle over the surface
which de?nes the structure. We analyse the generic case including the presence
of tangency points, i.e. points where two generators of the distribution and
their Lie bracket are linearly dependent.
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