Hilbert domains quasi-isometric to normed vector spaces

TL;DR

This paper proves that Hilbert domains quasi-isometric to normed vector spaces are necessarily convex polytopes, revealing a geometric rigidity property of such domains.

Contribution

It establishes a new characterization of Hilbert domains quasi-isometric to normed spaces as convex polytopes, linking geometric and metric properties.

Findings

Hilbert domains quasi-isometric to normed spaces are convex polytopes

Quasi-isometry implies convex polytope structure in this setting

Provides a rigidity result connecting metric and geometric properties

Abstract

We prove that a Hilbert domain which is quasi-isometric to a normed vector space is actually a convex polytope.