  We study the Steklov problem on hypersurfaces of revolution with two boundary
components in Euclidean space. In a recent article, the phenomenon of critical
length, at which a Steklov eigenvalue is maximized, was exhibited and multiple
questions were raised. In this article, we conjecture that, in any dimension,
there is a finite number of infinite critical length. To investigate this, we
develop an algorithm to efficiently perform numerical experiments, providing
support to our conjecture. Furthermore, we prove the conjecture in dimension $n
= 3$ and $n = 4$.
