Inserted: 25 jul 2018
Last Updated: 17 may 2020
Journal: Milan Journal of Mathematics
Published online:28 March 2020
We consider a relaxed notion of energy of non-parametric codimension one surfaces that takes account of area, mean curvature, and Gauss curvature. It is given by the best value obtained by approximation with inscribed polyhedral surfaces. The BV and measure properties of functions with finite relaxed energy are studied. Concerning the total mean and Gauss curvature, the classical counterexample by Schwarz-Peano to the definition of area is also analyzed.
Keywords: curvature of surfaces; polyhedral surfaces; bounded variation