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arxiv: 1906.03403 · v3 · pith:6QVS3WCP · submitted 2019-06-08 · math.MG

Smocked Metric Spaces and their Tangent Cones

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