Hamiltonien périodique de surface : désintégration de Floquet
Handle attaching in symplectic homology and the Chord Conjecture
Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...
Harmonicity of horizontally conformal maps and spectrum of the Laplacian.
Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms.