  We propose to use a simple observable, the fractional area of "hot spots" in
weak gravitational lensing mass maps which are detected with high significance,
to determine background cosmological parameters. Because these high-convergence
regions are directly related to the physical nonlinear structures of the
universe, they derive cosmological information mainly from the nonlinear regime
of density fluctuations. We show that in combination with future cosmic
microwave background anisotropy measurements, this method can place constraints
on cosmological parameters that are comparable to those from the redshift
distribution of galaxy cluster abundances. The main advantage of the statistic
proposed in this paper is that projection effects, normally the main source of
uncertainty when determining the presence and the mass of a galaxy cluster,
here serve as a source of information.
