The codisc radius capacity

Abstract

We define a capacity which measures the size of Weinstein tubular neighbourhoods 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. Moreover, we prove a generalization of Gromov's packing inequality concerning symplectic embeddings of the boundaries of two balls of equal radius into the open unit ball. If the interior components of the image spheres are disjoint, then the radii are less than the square root of one half. Furthermore, we introduce the spherical variant of the relative Gromov radius and prove finiteness for monotone Lagrangian tori in symplectic vector spaces.