Note on asymptotically conical expanding Ricci solitons

TL;DR

This paper demonstrates that any compact Riemannian manifold can serve as the sphere at infinity for an asymptotically conical gradient expanding Ricci soliton, at the level of formal expansions.

Contribution

It establishes a formal expansion framework linking compact Riemannian manifolds to asymptotically conical Ricci solitons.

Findings

Any compact Riemannian manifold can be the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton.

The result is shown at the level of formal expansions, not necessarily constructing explicit solutions.

Provides a new perspective on the asymptotic geometry of Ricci solitons.

Abstract

We show that at the level of formal expansions, any compact Riemannian manifold is the sphere at infinity of an asymptotically conical gradient expanding Ricci soliton.