Displaying similar documents to “Symplectic Capacities in Manifolds”

Singular Hamiltonian systems and symplectic capacities

Alfred Künzle (1996)

Banach Center Publications

Similarity:

The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation...

Symplectic embedding of thin discs into a ball

Takeo Nishinou (2004)

Mathematica Bohemica

Similarity:

We perform symplectic embeddings of ‘thin’ discs into a small ball in arbitrary dimension, using the symplectic folding construction.

Toric structures on near-symplectic 4-manifolds

David T. Gay, Margaret Symington (2009)

Journal of the European Mathematical Society

Similarity:

A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on...

On the number of components of the symplectic representatives of the canonical class

Stefano Vidussi (2007)

Journal of the European Mathematical Society

Similarity:

We show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincaré dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.