Viterbo's boundedness conjecture for the gamma metric

Let $N$ be a manifold, let $T^*N$ carry the cotangent-bundle structure, and let

denote the space of exact Lagrangians under consideration. For $r>0$, write

D_rT^*N={(q,p)\in T^*N:|p|\leq r}.

**Viterbo's conjecture.** For any $r>0$, the metric

is bounded on the space of exact Lagrangians contained in $D_rT^*N$. The conjecture would give uniform control of the gamma geometry for exact Lagrangians lying in a fixed cotangent disc bundle. The source presents it as open and uses it to derive further information about the generalized Birkhoff attractor.