Geodesic Interpolation on Sierpinski Gaskets
Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan, Luke G., Rogers
TL;DR
This paper explores geodesic interpolation and measure transport on Sierpinski gaskets, establishing a family of interpolating measures and an inequality, based on a detailed understanding of geodesics in fractal structures.
Contribution
It introduces a novel framework for convex interpolation and measure transport on fractal Sierpinski gaskets, extending geometric analysis to complex fractal spaces.
Findings
Description of a natural family of interpolating measures
Establishment of an interpolation inequality
Enhanced understanding of geodesics on Sierpinski gaskets
Abstract
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.
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