“…When the neck closes, the neck radius goes to zero and the principal curvature C 2,wl diverges. However, the mean curvature remains finite and satisfies the asymptotic equality in the limit of small R ne , [ 39 ] with the mean curvature M ne of the closed neck determined by the mean curvatures M l and M s of the two membrane segments, l and s , adjacent to the neck. Thus, as the neck closes, the positive singular contribution from the second principal curvature C 2,wl = 1/ R ne > 0 is cancelled by another negative contribution arising from the contour curvature C 1,wl , which corresponds to a singular catenoid.…”