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math.MG2012
Higher dimensional distortion of random complexes
Dominic Dotterrer
Using the random complexes of Linial and Meshulam, we exhibit a large family of simplicial complexes for which, whenever affinely embedded into Euclidean space, the filling areas o…
math.MG2012
The filling problem in the cube
Dominic Dotterrer
We prove an isoperimetric inequality for filling cellular cycles in a high dimensional cube with cellular chains. In addition, we provide a family of cubical cellular cycles for wh…