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Fragmented Hofer's geometry on Hameomorphism groups and its application
Morimichi Kawasaki
Stefan Mller posed the problem "Do Hofer's metrics on the group of Hamiltonian diffeomorphism and the one of Hamiltonian homeomorphisms (Hameomorphisms) correspo…
Fragmented Hofer's geometry
Morimichi Kawasaki
Hofer's norm (metric) is an important and interesting topic in symplectic geometry. In the present paper, we define fragmented Hofer's norms which are Hofer's norms controlled by f…
Heavy subsets and non-contractible trajectories
Morimichi Kawasaki
Entov and Polterovich defined heaviness for closed subsets of a symplectic manifold by using the Hamiltonian Floer theory on contractible trajectories. Heavy subsets are known to b…
Bavard's duality theorem on conjugation-invariant norms
Morimichi Kawasaki
Bavard proved a duality theorem between commutator length and quasimorphisms. Burago, Ivanov and Polterovich introduced the notion of a conjugation-invariant norm which is a genera…