  Consider a closed coisotropic submanifold $N$ of a symplectic manifold
$(M,\omega)$ and a Hamiltonian diffeomorphism $\phi$ on $M$. The main result of
this article states that $\phi$ has at least the cup-length of $N$ many
leafwise fixed points w.r.t. $N$, provided that it is the time-1-map of a
global Hamiltonian flow whose restriction to $N$ stays $C^0$-close to the
inclusion $N\to M$. If $(\phi,N)$ is suitably nondegenerate then the number of
these points is bounded below by the sum of the Betti-numbers of $N$. The
nondegeneracy condition is generically satisfied.
  This appears to be the first leafwise fixed point result in which neither
$\phi\big|_N$ is assumed to be $C^1$-close to the inclusion $N\to M$, nor $N$
to be of contact type or regular (i.e., "fibering"). It is optimal in the sense
that the $C^0$-condition on $\phi$ cannot be replaced by the assumption that
$\phi$ is Hofer-small.
