Optimal Transportation Networks: Models and Theory

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On the differentiability of Lipschitz functions with respect to measures in the Euclidean space (2014, background): “x ∈ E an approximate tangent space Tan(E, x).(6) The tangent bundle is actually characterized by the property that for every k-dimensional surface S of class C1 there holds Tan(E, x) = Tan(S, x) for H -a.”
Analysis of fungal networks (2012, background): “Many definitions of optimality yield treelike structures, with a single path connecting any two points (Sherman, 1981; Banavar et al., 1999, 2000a, b; Durand, 2006, 2007; Bohn and Magnasco, 2007; Bernot et al., 2008).”