Geodesic Interpolation on Sierpinski Gaskets

by Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan, Luke G. Rogers

We study the analogue of a convex interpolant of two sets on Sierpinski 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.

Arxiv preprint version