We consider a relaxed notion of energy of non-parametric codimensionone surfaces that takes into account area, mean curvature, and Gauss curvature.It is given by the best value obtained by approximation with inscribed polyhedralsurfaces. The BV and measure properties of functions with finite relaxedenergy are studied. Concerning the total mean and Gauss curvature, the classicalcounterexample by Schwarz-Peano to the definition of area is also analyzed.
Bounded variation and relaxed curvature of surfaces / Mucci, Domenico; Saracco, Alberto. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - (2020). [10.1007/s00032-020-00311-w]
Bounded variation and relaxed curvature of surfaces
Domenico Mucci;Alberto Saracco
2020
Abstract
We consider a relaxed notion of energy of non-parametric codimensionone surfaces that takes into account area, mean curvature, and Gauss curvature.It is given by the best value obtained by approximation with inscribed polyhedralsurfaces. The BV and measure properties of functions with finite relaxedenergy are studied. Concerning the total mean and Gauss curvature, the classicalcounterexample by Schwarz-Peano to the definition of area is also analyzed.
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