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arXiv · 1906.03403

Smocked Metric Spaces and their Tangent Cones

Christina Sormani·Demetre Kazaras·David Afrifa·Victoria Antonetti·Moshe Dinowitz·Hindy Drillick·Maziar Farahzad·Shanell George·Aleah Lydeatte Hepburn·Leslie Trang Huynh·Emilio Minichiello·Julinda Mujo Pillati·Srivishnupreeth Rendla·Ajmain Yamin
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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.

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Christina Sormani, Demetre Kazaras, David Afrifa, Victoria Antonetti, Moshe Dinowitz, Hindy Drillick, Maziar Farahzad, Shanell George, Aleah Lydeatte Hepburn, Leslie Trang Huynh, Emilio Minichiello, Julinda Mujo Pillati, Srivishnupreeth Rendla, Ajmain Yamin. 2019-06-08. Smocked Metric Spaces and their Tangent Cones. https://arxiv.org/abs/1906.03403

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