Calculus of Variations and Geometric Measure Theory
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D. Mucci

On the curvature energy of Cartesian surfaces

created by mucci on 18 Nov 2017
modified on 07 Feb 2021


Published Paper

Inserted: 18 nov 2017
Last Updated: 7 feb 2021

Journal: The Journal of Geometric Analysis
Year: 2021

Published online: 05 February 2021.

Links: Link to Enhanced PDF


We analyze the lower semicontinuous envelope of the curvature functional of Cartesian surfaces in codimension one. To this aim, following the approach by Anzellotti-Serapioni-Tamanini, we study the class of currents that naturally arise as weak limits of Gauss graphs of smooth functions. The curvature measures are then studied in the non-parametric case. Concerning homogeneous functions, some model examples are studied in detail. Finally, a new gap phenomenon is observed.

Keywords: Curvature of surfaces; Cartesian currents; Gauss graphs; Gap phenomenon


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