Willmore energy: Brief introduction and survey

The Willmore energy is a type of energy that is studied in differential geometry, physics and mechanics. It was first introduced by Siméon-Denis Poisson and Marie-Sophie Germain, independently, at the beginning of the nineteenth century, but its complete formalism was due to Thomas Willmore. In essence, this type of energy quantitatively measures the deviation of a surface from local sphericity. It is important to note that there is some ambiguity in the literature between the terms bending energy and Willmore energy, and different sources provide different definitions.