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.

On the Curvature Energy of Cartesian Surfaces / Mucci, D.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - (2021). [10.1007/s12220-020-00601-0]

On the Curvature Energy of Cartesian Surfaces

Mucci D.
2021

Abstract

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.
On the Curvature Energy of Cartesian Surfaces / Mucci, D.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - (2021). [10.1007/s12220-020-00601-0]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2888939
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact