By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor that is particularly well-suited for being extended to general varifolds of any dimension and codimension through regularization. The resulting approximate second fundamental forms are defined not only for piecewise-smooth surfaces, but also for datasets of very general type (like, e.g., point clouds). We obtain explicitly computable formulas for both weak and approximate curvature tensors, we exhibit structural properties and prove convergence results, and lastly we provide some numerical tests on point clouds that confirm the generality and effectiveness of our approach.

Weak and approximate curvatures of a measure: a varifold perspective / Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - ELETTRONICO. - 2022, 222:(2022), pp. 11298301-11298334. [10.1016/j.na.2022.112983]

Weak and approximate curvatures of a measure: a varifold perspective

Leonardi, Gian Paolo;
2022-01-01

Abstract

By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor that is particularly well-suited for being extended to general varifolds of any dimension and codimension through regularization. The resulting approximate second fundamental forms are defined not only for piecewise-smooth surfaces, but also for datasets of very general type (like, e.g., point clouds). We obtain explicitly computable formulas for both weak and approximate curvature tensors, we exhibit structural properties and prove convergence results, and lastly we provide some numerical tests on point clouds that confirm the generality and effectiveness of our approach.
2022
Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon
Weak and approximate curvatures of a measure: a varifold perspective / Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - ELETTRONICO. - 2022, 222:(2022), pp. 11298301-11298334. [10.1016/j.na.2022.112983]
File in questo prodotto:
File Dimensione Formato  
1-s2.0-S0362546X22001171-main.pdf

Solo gestori archivio

Descrizione: articolo pubblicato
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 4.21 MB
Formato Adobe PDF
4.21 MB Adobe PDF   Visualizza/Apri
1904.05930.pdf

Open Access dal 04/05/2023

Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Creative commons
Dimensione 4.42 MB
Formato Adobe PDF
4.42 MB Adobe PDF Visualizza/Apri

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: https://hdl.handle.net/11572/356901
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
  • OpenAlex ND
social impact