Smocked Metric Spaces and their Tangent Cones

2019/06/08 by Sormani, Christina, Kazaras, Demetre, Afrifa, David +11
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1906.03403

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.

Related

• SWIF Convergence of Smocked Metric Spaces
• Gromov-Hausdorff convergence and tangent cones of smocked spaces
• The Checkered Smocked Space and its Tangent Cone
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• A new survey: Cone metric spaces