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Abstract. This is a survey on the recent developments on steady gradi- ent Ricci solitons. In any dimension n ≥ 3, we constructed a new family of steady gradient Ricci solitons with positive curvature operator. In dimension three, these solitons are flying wings, as conjectured by Hamilton. We also proved that all 3D steady gradient Ricci solitons are O(2)-symmetric.
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This content will become publicly available on January 1, 2026
O(2)-symmetry of 3D steady gradient Ricci solitons
We prove that all 3D steady gradient Ricci solitons are O(2)-symmetric. The O(2)-symmetry is the most universal symmetry in Ricci flows with any type of symmetries. Our theorem is also the first instance of symmetry theorem for Ricci flows that are not rotationally symmetric. We also show that the Bryant soliton is the unique 3D steady gradient Ricci soliton with positive curvature that is asymptotic to a ray.
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- PAR ID:
- 10592694
- Publisher / Repository:
- Mathematical Sciences Publishers
- Date Published:
- Journal Name:
- Geometry & Topology
- Volume:
- 29
- Issue:
- 2
- ISSN:
- 1465-3060
- Page Range / eLocation ID:
- 687 to 789
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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