  We demonstrate that the above-threshold behavior of a laser can be strongly
affected by exceptional points which are induced by pumping the laser
nonuniformly. At these singularities, the eigenstates of the non-Hermitian
operator which describes the lasing modes coalesce. In their vicinity, the
laser may turn off even when the overall pump power deposited in the system is
increased. Such signatures of a pump- induced exceptional point can be
experimentally probed with coupled ridge or microdisk lasers.
