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