Multimetric Finsler geometry

Unicorns in Finsler Geometry

By unicorns, I am referring to those mythical single-horned horse-like creatures for which there are only rumoured sightings by a privileged few. A similar situation exists in Finsler differential geometry. There, one has the hierarchy Euclidean ⊂ Minkowskian & Riemannian ⊂ Berwald ⊂ Landsberg among five families of metrics, in which the first two inclusions are known to be proper by virtue of ...

The Geometry of Finsler Spaces

The term "Finsler space " evokes in most mathematicians the picture of an impenetrable forest whose entire vegetation consists of tensors. The purpose of the present lecture is to show that the association of tensors (or differential forms) with Finsler spaces is due to an historical accident, and that, at least at the present time, the fruitful and relevant problems lie in a different directio...

Spectral Variation, Normal Matrices, and Finsler Geometry

Medians and means in Finsler geometry

We investigate existence and uniqueness of p-means ep and the median e1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove that ep is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for p ≥ 2, a discretization of this path converges to ep. This provides an algorithm for dete...

Average control system and Finsler geometry

This talk will define an ”average control system” for system that have a conservative drift and a very small control. The prototype is low thrust orbital transfer of earth sattelites. Using averaging to treat small perturbations of integrable systems is not new; the originality here is that averaging can be performed before the variations of the control are decided, thus yielding really an ”ave...