  Let $v$ be a solution of the axially symmetric Euler equations (ASE) in a
finite cylinder in $\mathbb{R}^3$. We show that suitable blow-up limits of
possible velocity singularity and most self similar vorticity singularity near
maximal points off the vertical axis are two dimensional ancient solutions of
the Euler equation in either $\mathbb{R}^2 \times (-\infty, 0]$ or
$\mathbb{R}^2_+ \times (-\infty, 0]$. This reduces the search of off-axis
self-similar or other velocity blow-up solutions to a problem involving purely
2-dimensional Euler equations.
  Also, some asymptotic self-similar velocity blow-up and expected asymptotic
self-similar vorticity blow up scenario at the boundary appear to be ruled out.
On the other hand, this method may provide a path to velocity blow up if one
can construct certain stable ancient solutions to the 2-d Euler equation in the
half plane.
