Willmore energy

Willmore energy is a mathematical concept used to measure the "bending" or "curvature" of surfaces, particularly in shapes like membranes or soap films. It quantifies how much the surface deviates from being flat or minimal in energy. In a practical sense, surfaces with lower Willmore energy are more stable and efficient, like how a soap bubble adopts a rounded shape to minimize its surface area. This concept finds applications in fields such as materials science, biology, and computer graphics, helping to understand and model various natural and artificial structures.