Smocked Metric Spaces and their Tangent Cones
Metric Geometry
2020-09-02 v3
Abstract
We introduce the notion of a smocked metric spaces 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.
Cite
@article{arxiv.1906.03403,
title = {Smocked Metric Spaces and their Tangent Cones},
author = {Christina Sormani and Demetre Kazaras and David Afrifa and Victoria Antonetti and Moshe Dinowitz and Hindy Drillick and Maziar Farahzad and Shanell George and Aleah Lydeatte Hepburn and Leslie Trang Huynh and Emilio Minichiello and Julinda Mujo Pillati and Srivishnupreeth Rendla and Ajmain Yamin},
journal= {arXiv preprint arXiv:1906.03403},
year = {2020}
}
Comments
66 pages, 32 figures, original research by Prof. Sormani, Dr. Kazaras, and a team of students listed both above as authors and also within v1 at the tops of the sections that they specifically worked on, v2 has minor expository changes, v3 has minor technical revisions