On the Curvature Energy of Cartesian Surfaces

被引：0
|
作者：
Domenico Mucci
机构：
[1] Università di Parma,Dipartimento di Scienze Matematiche, Fisiche ed Informatiche
来源：
The Journal of Geometric Analysis | 2021年 / 31卷
关键词：
Curvature of surfaces; Cartesian currents; Gauss graphs; Gap phenomenon; 49Q45; 53A05; 49J45;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：8460 / 8519
页数：59
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