3D flying wings for any asymptotic cones

TL;DR

This paper constructs a family of 3D steady gradient Ricci solitons, called 3D flying wings, with asymptotic cones forming sectors of arbitrary angles, advancing understanding of geometric structures in Ricci flow.

Contribution

It introduces the novel concept of 3D flying wings, providing explicit examples of Ricci solitons with prescribed asymptotic cone sectors.

Findings

Existence of 3D steady gradient Ricci solitons with sector-shaped asymptotic cones.

Construction valid for all sector angles in (0, π).

Enhances the classification of Ricci solitons by asymptotic geometry.

Abstract

For every $\theta\in(0,\pi)$, we construct a 3D steady gradient Ricci soliton whose asymptotic cone is a sector with angle $\theta$, which is a called 3D flying wing.