3 problems

Let $(V,\xi)$ be a closed contact manifold, where $\xi$ is a cooriented contact structure, and let $\operatorname{Cont}_0(V,\xi)$ denote the identity component of its contactomorph…

Let $(N,\xi)$ be a contact manifold with a global contact form $\alpha$, and let $\psi$ be a contactomorphism. Say that $\psi$ has small oscillation energy when its oscillation ene…

Let $(M^{2n+1},\xi)$ be an overtwisted contact manifold. A positive loop of contactomorphisms is a loop generated by a strictly positive contact Hamiltonian. Folklore conjecture. O…