Small-energy isotopies of loose Legendrian submanifolds

We prove that for a closed Legendrian submanifold L of dimension n 2 with a loose chart of size , any Legendrian isotopy starting at L can be C 0 -approximated by a Legendrian isotopy with energy arbitrarily close to 1 2 .This in particular implies that the displacement energy of loose displaceable Legendrians is bounded by half the size of its smallest loose chart, which proves a conjecture of Dimitroglou Rizell and Sullivan (2020).