Disks extremal with respect to interpolation constants

We define a function $\mu$ from the set of sequences in the unit ball to ${\mathbb R}^*_+$ by taking the greatest lower bound of the reciprocal of the interpolating constant of the sequences of the disk which get mapped to the given sequence by a holomorphic mapping from the disk to the ball. Its properties are studied in the spirit of the work of Amar and Thomas.