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Proof of the main conjecture on $g$-areas

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  • In this paper, we prove the main conjecture on $g$-areas arising from [7]. That conjecture was announced by the first author in 2004. It~states that the $g$-area of any Hamiltonian diffeomorphism $\phi$ is equal to the positive Hofer pseudo-distance between $\phi$ and the subspace of Hamiltonian diffeomorphisms that can be expressed as a product of at most $g$ commutators.
    Mathematics Subject Classification: 53C15, 53D22, 53D40, 53D45, 57R58, 57S05, 58B20.


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