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math.DG2014★ 2 cited
Flat Norm Decomposition of Integral Currents
Sharif Ibrahim, Bala Krishnamoorthy, Kevin R. Vixie
Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary…
math.DG2014
Data-inspired advances in geometric measure theory: generalized surface and shape metrics
Sharif Ibrahim
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible b…
math.DG2011
Simplicial Flat Norm with Scale
Sharif Ibrahim, Bala Krishnamoorthy, Kevin R. Vixie
We study the multiscale simplicial flat norm (MSFN) problem, which computes flat norm at various scales of sets defined as oriented subcomplexes of finite simplicial complexes in a…