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May 2021 Smocked Metric Spaces and Their Tangent Cones
Christiana Sormani, Demetre Kazaras, David Afrifa, Victoria Antonetti, Moslie Dinowitz, Hindy Drillick, Maziar Farahzad, Shanell George, Aleah Lydeatte Hepburn, Leslie Trang Huynh, Emilio Minichiello, Julinda Mujo Pillati, Srivishnupreeth Rendla, Ajmain Yamin
Author Affiliations +
Missouri J. Math. Sci. 33(1): 27-99 (May 2021). DOI: 10.35834/2021/3301027

Abstract

We introduce the notion of a smocked metric space and explore the balls and geodesics in a collection of different smocked spaces. We find their rescaled Gromov-Hausdorff limits and prove these tangent cones at infinity exist, are unique, and are normed spaces. We close with a variety of open questions suitable for advanced undergraduates, masters students, and doctoral students.

Funding Statement

We are grateful to SCGP and CUNYGC for hosting our meeting. Prof. Sormani's research was funded in part by NSF DMS 1612049. Dr. Kazaras' research was funded by SB and SCGP. The students were unfunded volunteers completing the work for research credit only.

Citation

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Christiana Sormani. Demetre Kazaras. David Afrifa. Victoria Antonetti. Moslie Dinowitz. Hindy Drillick. Maziar Farahzad. Shanell George. Aleah Lydeatte Hepburn. Leslie Trang Huynh. Emilio Minichiello. Julinda Mujo Pillati. Srivishnupreeth Rendla. Ajmain Yamin. "Smocked Metric Spaces and Their Tangent Cones." Missouri J. Math. Sci. 33 (1) 27 - 99, May 2021. https://doi.org/10.35834/2021/3301027

Information

Published: May 2021
First available in Project Euclid: 4 June 2021

Digital Object Identifier: 10.35834/2021/3301027

Subjects:
Primary: 53C23
Secondary: 54E35

Keywords: Gromov-Hausdorff , Smocked Metric Space , tangent space

Rights: Copyright © 2021 University of Central Missouri, School of Computer Science and Mathematics

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Vol.33 • No. 1 • May 2021
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