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
Download PDF

This article is published open access under our Subscribe to Open model.

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