We study critical surfaces for a surface energy which contains the squared \(L^2\) norm of the difference of the mean curvature H and the spontaneous curvature \(c_o\), coupled to the elastic energy of the boundary curve. We investigate the existence of equilibria with \(H\equiv -c_o\). When \(c_o \geqslant 0\), we characterize those cases where the infimum of this energy is finite for topological annuli, and we find the minimizer in the cases that it exists. Results for topological disks are also given.

中文翻译：

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最小化具有弹性边界的弹性表面能的配置

我们研究临界表面的表面能，该表面能包含平均曲率H和自发曲率\（c_o \）之差的平方\（L ^ 2 \）范数，再加上边界曲线的弹性能。我们用\（H \ equiv -c_o \）研究均衡的存在。当\（c_o \ geqslant 0 \）时，我们描述了这种能量的极小值对于拓扑环是有限的那些情况，并且在存在极小值的情况下找到了极小值。还给出了拓扑磁盘的结果。