  There is a number of known constructions of quasimorphisms on Hamiltonian
groups. We show that on surfaces many of these quasimorphisms are not
compatible with the Hofer norm in a sense they are not continuous and not
Lipschitz. The only exception known to the author is the Calabi quasimorphism
on a sphere and the induced quasimorphisms on genus-zero surfaces.

Symplectic Geometry