Applications of discrete curvature have been around a while, for example this PDF [0] from 2003, so maybe this paper provides theoretical context for existing work.

[0] "Anisotropic Polygonal Remeshing"

Pierre Alliez, David Cohen-Steiner, Olivier Devillers, Bruno Lévy, Mathieu Desbrun

https://hal.inria.fr/inria-00071778/document