Abstract
In this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at 0 of Mather’s function, thus providing a negative answer to a question asked by Siburg [Duke Math. J. 92 (1998) 295-319]. However, we show that equality holds if one considers the asymptotic distance defined in Viterbo [Math. Ann. 292 (1992) 685-710].
Citation
Alfonso Sorrentino. Claude Viterbo. "Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms." Geom. Topol. 14 (4) 2383 - 2403, 2010. https://doi.org/10.2140/gt.2010.14.2383
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