Calculus of Variations and Geometric Measure Theory

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