On singular Lagrangian fibrations and applications to symplectic embeddings I

In this paper, we construct singular Lagrangian fibrations on some examples of disk cotangent bundles in dimensions 4 and 6. As an application, we show how this construction can be used to obtain toric domains in some cases. In particular, we recover results from Ferreira, Ramos, and Vicente on the Gromov width of the disk cotangent bundle of spheres of revolution, as well as results from Ramos on the Lagrangian bidisk. We also briefly discuss how this technique can be used to study symplectic embedding problems.