2000 character limit reached
Distortion from spheres into Euclidean space (2504.02276v1)
Published 3 Apr 2025 in math.MG and math.GN
Abstract: Any function from a round $n$-dimensional sphere of radius $r$ into $n$-dimensional Euclidean space must distort the metric additively by at least $\frac{2\pi r}{2 + \sqrt{3-2/n}}$. This is proved using a fixed-point theorem of Granas that generalizes the classical theorem of Borsuk--Ulam to set-valued functions.
Sponsored by Paperpile, the PDF & BibTeX manager trusted by top AI labs.
Get 30 days freePaper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.