Generic properties of von Kármán equations
Generic simplicity of eigenvalues for a Dirichlet problem of the bilaplacian operator.
Geodesic equations on diffeomorphism groups.
Geodesic reduction via frame bundle geometry.
Geodesics in the compactly supported Hamiltonian diffeomorphism group.
Geometry of compactifications of locally symmetric spaces
For a locally symmetric space , we define a compactification which we call the “geodesic compactification”. It is constructed by adding limit points in to certain geodesics in . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give for locally symmetric spaces. Moreover, has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...
Geometry on the group of Hamiltonian diffeomorphisms.
Global strong solutions in Sobolev or Lebesgue spaces to the incompressible Navier-Stokes equations in
Gradient flow for the one-dimensional Mumford-Shah functional
Gradient flows of non convex functionals in Hilbert spaces and applications
This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Group actions, gauge transformations, and the calculus of variations.
Groupe des difféomorphismes et espace de Teichmüller d'une surface
Groupes d’automorphismes de et équations différentielles
Groups of diffeomorphisms and Lie theory.
Hamiltonian loops from the ergodic point of view
Let be the group of Hamiltonian diffeomorphisms of a closed symplectic manifold . A loop is called strictly ergodic if for some irrational number the associated skew product map defined by is strictly ergodic. In the present paper we address the following question. Which elements of the fundamental group of can be represented by strictly ergodic loops? We prove existence of contractible strictly ergodic loops for a wide class of symplectic manifolds (for instance for simply connected...
Harmonic Functions of Polynomial Growth on Certain Complete Manifolds.
Heat kernel measure on central extension of current groups in any dimension.
Heterogeneous Riemannian manifolds.
Hofer’s metrics and boundary depth
We show that if is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of Hamiltonian diffeomorphisms of has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer’s metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in when satisfies...
Holonomy orbits of the snake charmer algorithm