Symplectic capacities of domains close to the ball and Banach-Mazur geodesics in the space of contact forms

Alberto Abbondandolo, Gabriele Benedetti, Oliver Edtmair

We prove that all normalized symplectic capacities coincide on smooth domains in ${\mathbb{C}}^n$ which are $C^2$-close to the Euclidean ball, whereas this fails for some smooth domai…