Weak and approximate curvatures of a measure: a varifold perspective

Autor:	Buet, Blanche, Leonardi, Gian Paolo, Masnou, Simon
Rok vydání:	2019
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Functional Analysis Mathematics - Numerical Analysis Primary: 49Q15. Secondary: 68U05 65D18
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.05930 Zobrazit plný text záznamu View this record from Arxiv