Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
Variational calculus on Lie algebroids
It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.
Variational characterization of equations of motion in bundles of embeddings.
In this paper we study variational principles for a general situation which includes free boundary problems with surface tension. Following [2], our main result concerns a variational principle in a infinite dimensional principal bundle of embeddings of a compact region D in a manifold M having the same dimension as D. By considering arbitrary variations, free boundary problems are included, while variations parallel to the boundary permit to consider fluid motion or flow of Hamiltonian vector fields...
Variational principles for differential equations with symmetries and conservation laws. II. Polynomial differential equations.
Variational principles for differential equations with symmetries and conservation laws. I. Second order scalar equations.
Variational problems for riemannian functionals and arithmetic groups
Variétés inertielles dans le cas non auto-adjoint. Applications aux variétés lentes