Metastability of Spherical Membranes in Supermembrane and Matrix Theory

Motivated by recent work we study rotating ellipsoidal membranes in the framework of the light-cone supermembrane theory. We investigate stability properties of these classical solutions which are important for the quantization of super membranes. We find the stability modes for all sectors of small multipole deformations. We exhibit an isomorphism of the linearized membrane equation with that of the SU(N) matrix model for every value of $N$. The boundaries of the linearized stability region are at a finite distance and they appear for finite size perturbations.