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ERA-MS

We prove a generalization of Gromov's packing inequality to symplectic embeddings of the boundaries of two balls such that the bounded components of the complements of the image spheres are disjoint. Moreover, we define a capacity which measures the size of Weinstein tubular neighborhoods of Lagrangian submanifolds. In symplectic vector spaces this leads to bounds on the codisc radius for any closed Lagrangian submanifold in terms of Viterbo's isoperimetric inequality. Furthermore, we introduce the spherical variant of the relative Gromov radius and prove its finiteness for monotone Lagrangian tori in symplectic vector spaces.

JMD

We prove that there exist periodic orbits on almost all compact regular energy
levels of a Hamiltonian function defined on a twisted cotangent bundle over
the two-sphere. As a corollary, given any Riemannian two-sphere and a magnetic
field on it, there exists a closed magnetic geodesic for almost all
kinetic energy levels.

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