JournalsjfgVol. 8, No. 2pp. 117–152

Geodesic interpolation on Sierpiński gaskets

  • Caitlin M. Davis

    University of Wisconsin-Madison, USA

  • Laura A. LeGare

    University of Notre Dame, USA

  • Cory W. McCartan

    Harvard University, Cambridge, USA

  • Luke G. Rogers

    University of Connecticut, Storrs, USA
Geodesic interpolation on Sierpiński gaskets cover
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Abstract

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].

Cite this article

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. 117–152

DOI 10.4171/JFG/100