On the injectivity radius and tangent cones at infinity of gradient Ricci solitons

TL;DR

This paper investigates the geometric properties of gradient Ricci solitons, focusing on injectivity radius bounds, tangent cones at infinity, and asymptotic volume ratios to deepen understanding of their structure.

Contribution

It provides new lower-bound estimates for injectivity radius and analyzes tangent cones at infinity for gradient Ricci solitons, advancing geometric understanding.

Findings

Established lower bounds for injectivity radius in certain manifolds

Characterized tangent cones at infinity for specific gradient Ricci solitons

Analyzed asymptotic volume ratios of gradient Ricci solitons

Abstract

A lower-bound estimate of injectivity radius for complete Riemannian manifolds is discussed in a pure geometric viewpoint and is applied to study tangent cones at infinity of certain gradient Ricci solitons. We also study the asymptotic volume ratio of gradient Ricci solitons.