Geodesic interpolation on Sierpiński gaskets

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

doi:10.4171/JFG/100

Geodesic interpolation on Sierpiński gaskets

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

Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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].

Original language	English (US)
Pages (from-to)	117-152
Number of pages	36
Journal	Journal of Fractal Geometry
Volume	8
Issue number	2
DOIs	https://doi.org/10.4171/JFG/100
State	Published - 2021

All Science Journal Classification (ASJC) codes

Geometry and Topology
Applied Mathematics

Access to Document

10.4171/JFG/100

Cite this

@article{cfec862ecd514920908e44c395c59e8d,

title = "Geodesic interpolation on Sierpi{\'n}ski gaskets",

abstract = "We study the analogue of a convex interpolant of two sets on Sierpi{\'n}ski 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].",

author = "Davis, \{Caitlin M.\} and LeGare, \{Laura A.\} and McCartan, \{Cory W.\} and Rogers, \{Luke G.\}",

note = "Publisher Copyright: {\textcopyright} 2021 European Mathematical Society Published by EMS Press This work is licensed under a CC BY 4.0 license.",

year = "2021",

doi = "10.4171/JFG/100",

language = "English (US)",

volume = "8",

pages = "117--152",

journal = "Journal of Fractal Geometry",

issn = "2308-1309",

publisher = "European Mathematical Society Publishing House",

number = "2",

}

TY - JOUR

T1 - Geodesic interpolation on Sierpiński gaskets

AU - Davis, Caitlin M.

AU - LeGare, Laura A.

AU - McCartan, Cory W.

AU - Rogers, Luke G.

PY - 2021

Y1 - 2021

N2 - 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].

AB - 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].

UR - https://www.scopus.com/pages/publications/85107145732

UR - https://www.scopus.com/pages/publications/85107145732#tab=citedBy

U2 - 10.4171/JFG/100

DO - 10.4171/JFG/100

M3 - Article

AN - SCOPUS:85107145732

SN - 2308-1309

VL - 8

SP - 117

EP - 152

JO - Journal of Fractal Geometry

JF - Journal of Fractal Geometry

IS - 2

ER -

Geodesic interpolation on Sierpiński gaskets

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this