This paper derives general formulae for normalized error surface curvatures by using the constant modulus algorithm (CMA), the multimodulus algorithm(MMA), and two well known blind carrier phase recovery algorithms (CPRA) at the stationary points with arbitrary two-dimensional symmetric signal constellations. Based on the derived error surface curvatures, both the performance of the CMA followed by a blind CPRA and the performance of the MMA are forecasted and evaluated in terms of blind equalizer convergence and carrier phase recovery.