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Paper detail

Bounded variation and relaxed curvature of surfaces

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.

preprint2020arXivOpen access
Domenico MucciAlberto Saracco
math.DG
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Domenico MucciAlberto Saracco

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