What is the minimal surface connecting two circles that don't lie in parallel planes?
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I'm curious about a general answer for oblique planes, but specifically, I'm interested in the case where one circle's axis is perpendicular to the other's, and its center lies on the other's axis. To be precise, let $C_1$ be the unit circle in the $XY$ plane, and $C_2$ be a circle of radius $r$ , center $(0, 0, h)$ , with axis parallel to the $x$ axis. Thinking of these two circles as a sort of minimalist sketch of a signet ring, what is the minimal surface that might be thought of as the convex hull of the ring? I'm hoping for an analytical solution, but also curious about answering this kind of question computationally.
minimal-surfaces
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