We study equilibrium surfaces for an energy which is a linear combination of the area and a second term which measures the bending and twisting of the boundary. Specifically, the twisting energy is given by the twisting of the Darboux frame. This energy is a modification of the Euler–Plateau functional considered by Giomi and Mahadevan (2012, Proc. R. Soc. A 468, 1851–1864), and a natural special case of the Kirchhoff–Plateau energy considered by Biria and Fried (2014, Proc. R. Soc. A 470, 20140368; 2015, Int. J. Eng. Sci. 94, 86–102).

中文翻译：

---

具有弹性和部分弹性边界的最小曲面

我们研究能量的平衡面，能量是面积和测量边界弯曲和扭曲的第二项的线性组合。具体来说，扭转能量是由达布框架的扭转给出的。这种能量是 Giomi 和 Mahadevan (2012,过程。R. Soc。一种468, 1851–1864)，以及 Biria 和 Fried (2014,过程。R. Soc。一种470、20140368；2015年，诠释。J.工程。科学。94, 86–102)。