On one blow up point solutions to the critical nonlinear Schrodinger equation

We consider the L-2 critical nonlinear Schrodinger equation iu(t) = -Delta u - vertical bar u vertical bar 4/Nu in the energy space H-1. In the series of papers [11-15,18], we studied finite time blow up solutions for which lim(t up arrow T<+infinity) vertical bar del u(t)vertical bar(L2) = +infinity and proved classification results of the blow up dynamics for the specific class of small super critical L-2 mass initial data. We extend these results here to a wider class of finite time blow up solutions corresponding to the ones which accumulate at one point exactly the ground state mass. In particular, we prove the existence and stability of large L-2 Mass log-log type solutions which are believed to describe the generic blow up dynamics.