Partially motivated by the study of topological Hamiltonian dynamics, we prove the following -continuity of the Lagrangian capacity function :
as , provided the ’s satisfy for some and a closed subset with nonempty interior. We also provide an estimate of the capacity in terms of the -distance of and the subset relative to .
"Hamiltonian -continuity of Lagrangian capacity on the cotangent bundle." Kyoto J. Math. 57 (3) 613 - 636, September 2017. https://doi.org/10.1215/21562261-2017-0008