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Geodesic interpolation on Sierpiński gaskets. (English) Zbl 1470.28008

Summary: 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.

MSC:

28A80 Fractals
05C12 Distance in graphs
26D15 Inequalities for sums, series and integrals
30L05 Geometric embeddings of metric spaces
49Q22 Optimal transportation
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