Symplectically convex and symplectically star-shaped curves: a variational problem (Q6601726)

The authors propose a generalization of the two-dimensional notions of being convex and being star-shaped to symplectic vector spaces. The main idea is to study variational problems that can be reduced back to two dimensions. For a range of the family parameters the extremal points of the variational problem are multiply traversed conics. For this case, conditions on non-trivial first and second order deformations are derived.\N\NThe paper is well written and all technical steps are explained in a clear manner. The reference list is well chosen.\N\NFor the entire collection see [Zbl 1515.53004].