A topological pinching for the injectivity radius of a compact surface in S^3 and in H^3

TL;DR

This paper introduces a topological pinching condition that provides bounds on the injectivity radius of compact embedded surfaces in spherical and hyperbolic spaces, enhancing understanding of their geometric properties.

Contribution

It presents a novel topological pinching criterion that relates the injectivity radius to the surface's topology in S^3 and H^3, extending previous geometric bounds.

Findings

Establishes bounds on the injectivity radius based on topological conditions.

Applies the pinching criterion to surfaces in both spherical and hyperbolic geometries.

Provides new insights into the geometric structure of embedded surfaces.

Abstract

It is given a topological pinching for the injectivity radius of a compact embedded surface either in the sphere or in the hyperbolic space