Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem (Q6564810)

The authors solve a modified Kirchhoff-Plateau problem for existing a minimal surface spanning a given curve. In contrast to the Plateau problem, the Kirchhoff-Plateau problem concerns the equilibrium shape of a system of a closed Kirchhoff rod spanned by an area-minimizing surface. The Euler-Lagrange equations for an elastic rod spanned by a soap film are explicitly derived. Three cases of the equations specifying the shape of the cross-section are considered: elliptic with fixed area, elliptic with dilation of the horizontal semi-axis from the equilibrium configuration and oval cross-section with a fixed area.