arXiv
Open Access
2025
Uniqueness of asymptotically cylindrical steady gradient Ricci solitons
Michael B. Law
Abstrak
We show that the Bryant soliton is the unique asymptotically cylindrical steady gradient Ricci soliton, in any dimension $n \geq 3$ and without any curvature assumptions. This generalizes a celebrated theorem of Brendle. We also prove that any steady gradient Ricci soliton asymptotic to a cylinder over the homogeneous lens space $\mathbb{S}^{2m+1}/\mathbb{Z}_k = L_{m,k}$, for $m \geq 1$ and $k \geq 3$, is a noncollapsed Appleton soliton on the complex line bundle $O(-k)$ over $\mathbb{CP}^m$. Specializing to dimension 4, we classify steady gradient Ricci soliton singularity models on smooth orbifolds with tangent flows at infinity of the form $(SU(2)/Γ) \times \mathbb{R}$.
Topik & Kata Kunci
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Michael B. Law
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2025
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- arXiv
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