  We are concerned with the similarity problem for Cowen-Douglas operator
tuples. The unitary equivalence counterpart was already investigated in the
1970's and geometric concepts including vector bundles and curvature appeared
in the description. As the Cowen-Douglas conjecture show, the study of the
similarity problem has not been so successful until quite recently. The latest
results reveal the close correlation between complex geometry, the corona
problem, and the similarity problem for single Cowen-Douglas operators. Without
making use of the corona theorems that no longer hold in the multi-variable
setting, we prove that the single operator results for similarity remain true
for commuting Cowen-Douglas operator tuples as well.
