The Checkered Smocked Space and its Tangent Cone

Abstract

Smocked metric spaces were first defined in arXiv:1906.03403 and it was proved that if a norm on the Euclidean space uniformly estimates the pseudometric of a smocked metric space, then the tangent cone at infinity is unique and is a norm vector space with that estimating norm. In this paper, we explicitly calculate the norm approximating the pseudometric of the checkered smocked space and find the tangent cone at infinity.