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math.CA2013★ 18 cited
Multiscale analysis of 1-rectifiable measures: necessary conditions
Matthew Badger, Raanan Schul
We repurpose tools from the theory of quantitative rectifiability to study the qualitative rectifiability of measures in , . To each locally finite Borel measur…
math.MG2013★ 3 cited
The traveling salesman problem in the Heisenberg group: upper bounding curvature
Sean Li, Raanan Schul
We show that if a subset in the Heisenberg group (endowed with the Carnot-Carathéodory metric) is contained in a rectifiable curve, then it satisfies a modified analogue of Pet…