Geodesic interpolation on Sierpiński gaskets

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

doi:10.4171/jfg/100

JournalsjfgVol. 8, No. 2pp. 117–152

Geodesic interpolation on Sierpiński gaskets

Caitlin M. Davis
University of Wisconsin-Madison, USA
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Laura A. LeGare
University of Notre Dame, USA
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- zbMATH Open
Cory W. McCartan
Harvard University, Cambridge, USA
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- zbMATH Open
Luke G. Rogers
University of Connecticut, Storrs, USA
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- zbMATH Open

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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