Numerical equilibrium shapes of a curvature-based membrane functional

Dataset accompanying the 14th Socratic Lectures conference proceedings contribution on curvature-based membrane functionals: Equivalent Characterisations of Singularity in Curvature-Coupled Membrane Functionals. It contains numerically computed axisymmetric equilibrium shapes under prescribed geometric constraints, illustrating representative stationary configurations across parameter regimes. Volume to area ratios and average mean curvatures: (a) v = 0.9920, ⟨h⟩ = 1.022, (b) v = 0.9500, ⟨h⟩ = 1.1324, (c) v = 0.9500, ⟨h⟩ = 1.1664, (d) v = 0.7325, ⟨h⟩ = 1.1473, (e) v = 0.6950, ⟨h⟩ = 1.2380, (f) v = 0.6950, ⟨h⟩ = 1.1120, (g) v = 0.4950, ⟨h⟩ = 1.7379, (h) v = 0.9500, ⟨h⟩ = 1.0165本数据集配套于收录于第14届苏格拉底讲座（Socratic Lectures）会议论文集的研究文章，该文章题为《曲率耦合膜泛函中奇点的等价表征》（Equivalent Characterisations of Singularity in Curvature-Coupled Membrane Functionals）。数据集包含在指定几何约束下通过数值计算得到的轴对称平衡形貌，展示了不同参数区间内的典型驻定构型。 体积面积比与平均曲率： (a) v = 0.9920, ⟨h⟩ = 1.022；(b) v = 0.9500, ⟨h⟩ = 1.1324；(c) v = 0.9500, ⟨h⟩ = 1.1664；(d) v = 0.7325, ⟨h⟩ = 1.1473；(e) v = 0.6950, ⟨h⟩ = 1.2380；(f) v = 0.6950, ⟨h⟩ = 1.1120；(g) v = 0.4950, ⟨h⟩ = 1.7379；(h) v = 0.9500, ⟨h⟩ = 1.0165