C^0-limits of Legendrian submanifolds

Abstract: Consider a sequence of contactomorphisms whose $C^0$-limit is a homeomorphism, and a Legendrian submanifold whose limiting image under this sequence is a smooth submanifold. I will show that the limit is in fact Legendrian, and moreover, when the contact manifold is 3-dimensional,  the limit is contactomorphic to the initial Legendrian knot.

This is joint work with Georgios Dimitroglou Rizell.