  We propose a method for deriving a dynamical lower bound on $\Omega$ from
diverging flows in low-density regions, based on the fact that large outflows
are not expected in a low-$\Omega$ universe. The velocities are assumed to be
induced by gravity from small initial fluctuations, but no assumptions are made
regarding their exact Gaussian nature, galaxy biasing, or $\Lambda$. The
derivatives of a diverging velocity field infer a nonlinear approximation to
the mass density, which is an overestimate when the true value of $\Omega$ is
assumed. This inferred density can become ridiculously negative when the
assumed $\Omega$ is too low, thus bounding $\Omega$. Observed radial peculiar
velocities of galaxies allow the \pot\ procedure to recover the required
velocity field, Gaussian smoothed at $1200\kms$. The density and the associated
errors are then inferred for different values of $\Omega$, searching for a void
which shows negative inferred density with high confidence. A preliminary
application to data in a southern void indicates that $\Omega\leq 0.3$ can be
ruled out at the $2.4$-sigma level. A detailed study of possible systematic
errors is under way.
