Lengths of Reeb chords and Viterbo restriction

We develop a version of Viterbo restriction map $SH(W)\to SH(T^{*}\Lambda)$ whenever $\Lambda$ is embedded as a Legendrian in the ideal boundary of $W$ without any Reeb chords for some contact form, generalizing earlier work in this direction by Zhengyi Zhou. Using this, we prove that, if $W=T^{*}M$ and $M$ is covered by a product of spheres (e.g., the $n$-torus), then all compact Legendrians $\Lambda\subset ST^{*}M$ admit a Reeb chord for every choice of contact form $ST^{*}M$. This is based on joint work with Filip Broćić.