On the Boundary Injectivity Radius of Buser-Colbois-Dodziuk-Margulis Tubes

TL;DR

This paper establishes a lower bound for the boundary injectivity radius of certain geometric structures called Margulis tubes, depending only on dimension and curvature bounds, advancing understanding of their geometric properties.

Contribution

It provides a new lower bound estimate for the boundary injectivity radius of Margulis tubes with smooth boundary, based solely on dimension and curvature bounds.

Findings

Lower bound depends only on dimension and curvature

Estimate applies to Buser-Colbois-Dodziuk constructed tubes

Enhances understanding of geometric properties of Margulis tubes

Abstract

We give a lower bound on the boundary injectivity radius of the Margulis tubes with smooth boundary constructed by Buser, Colbois, and Dodziuk. This estimate depends on the dimension and a curvature bound only.