We study the analogue of a convex interpolant of two sets on Sierpiński gaskets and an associated notion of measure transport. The structure of a natural family of interpolating measures is described and an interpolation inequality is established. A key tool is a good description of geodesics on these gaskets, some results on which have previously appeared in the literature [19, 17, 16, 11].
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Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan, Luke G. Rogers, Geodesic interpolation on Sierpiński gaskets. J. Fractal Geom. 8 (2021), no. 2, pp. 117–152DOI 10.4171/JFG/100