On the effect of projections on convergence peak counts and Minkowski
  functionals
  The act of projecting data sampled on the surface of the celestial sphere
onto a regular grid on the plane can introduce error and a loss of information.
This paper evaluates the effects of different planar projections on
non-Gaussian statistics of weak lensing convergence maps. In particular we
investigate the effect of projection on peak counts and Minkowski Functionals
(MFs) derived from convergence maps and the suitability of a number of
projections at matching the peak counts and MFs obtained from a sphere. We find
that the peak counts derived from planar projections consistently overestimate
the counts at low SNR thresholds and underestimate at high SNR thresholds
across the projections evaluated, although the difference is reduced when
smoothing of the maps is increased. In the case of the Minkowski Functionals,
V0 is minimally affected by projection used, while projected V1 and V2 are
consistently overestimated with respect to the spherical case.
