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.
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.
"Smocked Metric Spaces and Their Tangent Cones." Missouri J. Math. Sci. 33 (1) 27 - 99, May 2021. https://doi.org/10.35834/2021/3301027