We consider closed subsets of a noncompact symplectic manifold and determine when they can be removed by a symplectomorphism, in which case we say the subsets are symplectically excisable. We prove that, in the case of a ray and more generally, the embedding of the epigraph of a lower semi-continuous function, there is a time-independent Hamiltonian flow that excises it from a noncompact symplectic manifold.

Another interesting question is: if a set can be removed by a diffeomorphism, is it symplectically excisable? A counterexample is a wall with a hole (as the complement of the symplectic camel space by McDuff--Traynor) in $\mathbb{R}^{2n}$. We are interested in more examples and non-examples, and open problems related to symplectic excision.