Isolated singularities of extrema of geometric variational problems

1985 ◽  
pp. 206-277 ◽  
Author(s):  
Leon Simon
Keyword(s):  
Variational Problems ◽  
Isolated Singularities ◽  
Geometric Variational Problems

scholarly journals Discretization and Approximation of Surfaces Using Varifolds

2018 ◽  
Vol 3 (1) ◽  
pp. 28-56 ◽  
Author(s):  
Blanche Buet ◽  
Gian Paolo Leonardi ◽  
Simon Masnou
Keyword(s):  
Computational Geometry ◽  
Point Clouds ◽  
Variational Problems ◽  
Numerical Tests ◽  
Discrete Surfaces ◽  
Geometric Variational Problems

Abstract We present some recent results on the possibility of extending the theory of varifolds to the realm of discrete surfaces of any dimension and codimension, for which robust notions of approximate curvatures, also allowing for singularities, can be defined. This framework has applications to discrete and computational geometry, as well as to geometric variational problems in discrete settings. We finally show some numerical tests on point clouds that support and confirm our theoretical findings.

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