It is proved that the number of leafwise fixed points of a Hamiltonian diffeomorphism \(\phi\) of a geometrically bounded symplectic manifold is bounded below by the sum of the \(\mathbb Z_2\)-Betti numbers of the closed, regular coisotropic submanifold \(N\), provided that the Hofer distance between \(\phi\) and the identity is small enough and the pair \((N,\phi)\) is non-degenerate. Moreover, the bound is optimal if there exists a \(\mathbb Z_2\)-perfect Morse function on \(N\). As an application, a presymplectic non-embedding result is proved.
A version of the Arnold-Givental conjecture for coisotropic submanifolds is analyzed.