Asymptotic estimates and compactness of expanding gradient Ricci solitons

TL;DR

This paper studies the asymptotic behavior and compactness properties of expanding gradient Ricci solitons, providing sharp decay estimates and a compactness theorem for nonnegatively curved cases.

Contribution

It offers new sharp decay rate estimates for conical expanding gradient Ricci solitons and establishes a compactness theorem for nonnegatively curved cases.

Findings

Sharp decay rates to the asymptotic cone in generic and Ricci flat cases

A compactness theorem for nonnegatively curved expanding gradient Ricci solitons

Enhanced understanding of the asymptotic geometry of Ricci solitons

Abstract

We first investigate the asymptotics of conical expanding gradient Ricci solitons by proving sharp decay rates to the asymptotic cone both in the generic and the asymptotically Ricci flat case. We then establish a compactness theorem concerning nonnegatively curved expanding gradient Ricci solitons.