On the existence of Hamiltonian 4-manifolds with a contact type boundary

While the Hamiltonian group actions on closed symplectic manifolds have been widely explored throughout the last couple of decades, the study on Hamiltonian group actions on symplectic manifolds with a contact type boundary has started only recently, with the work by Niederkrüger and the author [MN]. In this note we pursue this study by presenting several methods to construct such Hamiltonian circle manifolds in dimension 4.