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Smocked Metric Spaces and their Tangent Cones

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

Smocked Metric Spaces and their Tangent Cones

classification math.MG
keywords spacessmockedconesmetricstudentstangentadvancedballs
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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