Complete Ricci solitons via estimates on the soliton potential

TL;DR

This paper develops growth estimates for the soliton potential on cohomogeneity one manifolds, enabling the construction of new complete Ricci solitons and offering a novel approach to existing systems.

Contribution

It introduces a new growth estimate for the soliton potential, facilitating the construction of continuous families of Ricci solitons and providing a unified approach to known examples.

Findings

Constructed new families of steady and expanding Ricci solitons

Provided growth estimates applicable to a broad class of manifolds

Presented a different method for analyzing the two summands system

Abstract

In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the set-ups of L\"u-Page-Pope and Dancer-Wang. It also provides a different approach to the two summands system which applies to all known geometric examples.