Menger curvature and Lipschitz parametrizations in metric spaces

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Regularizing and self-avoidance effects of integral Menger curvature (2010, unknown): “2 Generalizations of this result to metric spaces were proved by Hahlomaa [16,17]; see also recent work of Schul [28].”
On rectifiable curves with Lp-bounds on global curvature: self-avoidance, regularity, and minimizing knots (2007, background): “these sets are essentially contained in a union of Lipschitz graphs; for p = 2 see [33], and for a more general setting in metric spaces see [25], [26].”
Subsets of rectifiable curves in Hilbert space-the analyst’s TSP (2006, methodology): “Remark 1.6. We would like to note recent independent work done by Immo Hahlomaa (see [ Hah05 ]) containing a generalization of Theorem 1.5 to the setting of Metric Spaces! (Where one needs to use Menger curvature to define β .) There is also work by Ferrari, Franchi and Pajot for a version of this t”
High-Dimensional Menger-Type Curvatures—Part II: d-Separation and a Menagerie of Curvatures (2008, methodology): “Discrete Curvatures of General Metric Spaces Immo Hahlomaa [26] has formed a Menger-type curvature of one-regular measures in metric spaces using the Gromov product.”