Structure at infinity of expanding gradient Ricci soliton

TL;DR

This paper investigates the geometric structure at infinity of expanding gradient Ricci solitons in higher dimensions, showing they predominantly exhibit a cone structure at infinity under certain curvature conditions.

Contribution

It establishes that expanding gradient Ricci solitons with finite asymptotic curvature ratio have a cone structure at infinity, without assuming curvature sign conditions.

Findings

Proves cone structure at infinity for these solitons

Works in dimensions greater than two

Does not require curvature sign assumptions

Abstract

We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.