On the existence of geodesics in static Lorentz manifolds with singular boundary
On the minimizers of the Möbius cross energy of links.
On the Number of Closed Geodesics on Projective Spaces.
On the Resolution of Degenerate Closed Geodescis.
On the transversal distribution and the complete figure in the second order multiple integral problem in the calculus of variations.
Path functionals over Wasserstein spaces
Given a metric space we consider a general class of functionals which measure the cost of a path in joining two given points and , providing abstract existence results for optimal paths. The results are then applied to the case when is aWasserstein space of probabilities on a given set and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures and by means of finite cost paths are given.
Periodic geodesics generator.
Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds
Quand deux sous-variétés sont forcées par leur géométrie à se rencontrer
Quelques notions simples en géométrie riemannienne et leurs applications aux feuilletages compacts.
Restriction de la distance géodésique à un arc et rigidité
Shapes of spheres of special nonholonomic left-invariant intrinsic metrics on some Lie groups.
Stability of the Cut Locus in Dimensions Less Than or Equal to 6.
Structures symplectiques faibles et intégrabilité globale de certains systèmes hamiltoniens
Subriemannian geodesics of Carnot groups of step 3
In Carnot groups of step ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.
The Bonnet-Meyers theorem is true for Riemann Hilbert Manifolds.
The Critical Points Theory for the Closed Geodesics Problem.
The Cusp Catastrophe of Thom in the Bifurcation of Minimal Surfaces.
The Free Loop Space of Globally Symmetric Spaces.
The rectifiable distance in the unitary Fredholm group
Let = u: u unitary and u-1 compact stand for the unitary Fredholm group. We prove the following convexity result. Denote by the rectifiable distance induced by the Finsler metric given by the operator norm in . If and the geodesic β joining u₀ and u₁ in satisfy , then the map is convex for s ∈ [0,1]. In particular, the convexity radius of the geodesic balls in is π/4. The same convexity property holds in the p-Schatten unitary groups = u: u unitary and u-1 in the p-Schatten class...