From a Reeb orbit trap to a Hamiltonian plug

We present a simple construction of a plug for Hamiltonian flows on hypersurfaces of dimension at least five by doubling a trap for Reeb orbits.Comment: 6 page

Trapped Reeb orbits do not imply periodic ones

We construct a contact form on R^{2n+1}, n at least 2, equal to the standard contact form outside a compact set and defining the standard contact structure on all of R^{2n+1}, which has trapped Reeb orbits, including a torus invariant under the Reeb flow, but no closed Reeb orbits. This answers a question posed by Helmut Hofer.Comment: 6 page

Isoperimetric Inequalities for Minimal Submanifolds in Riemannian Manifolds: A Counterexample in Higher Codimension

For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small singular set. There is the natural question if a similar result is true for submanifolds of higher codimension. Specifically, B.White asked if the non-existence of an isoperimetric inequality for k-varifolds implies the existence of a nonzero, stationary, integral k-varifold. We present examples showing that this is not true in codimension greater than two. The key step is the construction of a Riemannian metric on the closed four-dimensional ball B with the following properties: (1) B has strictly convex boundary. (2) There exists a complete nonconstant geodesic. (3) There does not exist a closed geodesic in B.Comment: 11 pages, We changed the title and added a section that exhibits the relation between our example and the question posed by Brian White concerning isoperimetric inequalities for minimal submanifold