Best rank-one approximation ratio of higher-order tensors

For a higher-order tensor, its distance to the set of rank-one tensors
is an important quantity of interest from several perspectives.
Similar as for matrices, the relative distance is determined by the
ratio of the spectral and Frobenius norm of the tensor. The minimal
possible ratio of these norms hence measures the largest possible
relative distance, and is called the best rank-one approximation ratio
of the tensor space under consideration. Its precise value is only
known in special cases and hard to determine in general. In the talk,
we review this problem and present some recent results on the minimal
norm ratio.