Symplectic embeddings of ellipsoids into polydiscs of different capacities.

This paper addresses a fundamental problem in symplectic geometry: the existence and properties of symplectic embeddings between different geometric domains. Specifically, the authors study the conditions under which an ellipsoid can be symplectically embedded into a polydisc, focusing on cases with differing capacities. These types of embedding problems are highly relevant to understanding the rigidity phenomena in symplectic geometry and have connections to the packing problem in phase space, which can be important for optimal control and understanding the limits of Hamiltonian dynamics.