Many known quasimorphisms on surfaces fail to be continuous or Lipschitz in the Hofer norm, except for the Calabi quasimorphism on the sphere and induced versions on genus-zero surfaces.
On the L^p -geometry of autonomous H amiltonian diffeomorphisms of surfaces
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Quasimorphisms on surfaces and continuity in the Hofer norm
Many known quasimorphisms on surfaces fail to be continuous or Lipschitz in the Hofer norm, except for the Calabi quasimorphism on the sphere and induced versions on genus-zero surfaces.