Two-dimensional gradient Ricci solitons revisited

TL;DR

This paper completes the classification of non-compact two-dimensional gradient Ricci solitons, establishing bounded curvature for complete cases and providing new examples of expanding solitons with negative curvature that are topologically disks.

Contribution

It finalizes the classification of 2D non-compact gradient Ricci solitons and introduces new examples of expanding solitons with negative curvature.

Findings

Complete 2D gradient Ricci solitons have bounded curvature

Existence of non-hyperbolic, topologically disk-shaped expanding solitons with negative curvature

Abstract

In this note, we complete the classification of the geometry of non-compact two-dimensional gradient Ricci solitons. As a consequence, we obtain two corollaries: First, a complete two-dimensional gradient Ricci soliton has bounded curvature. Second, we give examples of complete two-dimensional expanding Ricci solitons with negative curvature that are topologically disks and are not hyperbolic space.