The Doubly Connected Minimal Surfaces Between Two Circles In Parallel Planes

In this article, we revisit some results published by several mathematicians regarding existence and non-existence of doubly connected minimal surfaces between two circles in parallel planes. In particular, we propose new analytical interpretations and results for catenoidal solutions formed between two coaxial circles in parallel planes of arbitrary radii. We conclude by discussing the nature of the pair of the catenoidal solutions that arise from our proposed algorithm.