Introduces joint upper Banach densities for plane sets and proves a cross-set distance realization theorem plus maximal VC dimension for families of scaled curve translates with non-vanishing curvature.
do Carmo.Differential Geometry of Curves and Surfaces: Revised and Updated
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Joint upper Banach density, VC dimensions and Euclidean point configurations
Introduces joint upper Banach densities for plane sets and proves a cross-set distance realization theorem plus maximal VC dimension for families of scaled curve translates with non-vanishing curvature.