Higher-dimensional flying wing Steady Ricci Solitons
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917229675675648 |
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| author | Chan, Pak-Yeung Lai, Yi Lee, Man-Chun |
| author_facet | Chan, Pak-Yeung Lai, Yi Lee, Man-Chun |
| contents | For any $n\geq 4$, we construct an $(n-2)$-parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor at a critical point of the soliton potential. Among them lies an $(n-3)$-parameter subfamily of non-collapsed solitons. These solitons generalized the flying wings constructed by the second named author and produced new examples of steady gradient Ricci solitons with non-negative curvature operator for $n\geq 4$. Our approach is based on constructing continuous families of Ricci flows smoothing emanating from continuous families of spherical polyhedra which still preserves symmetry.
This is built upon a new stability result of Ricci flows with scaling invariant estimates. As another application of the method, we prove the stability of asymptotically conical expanding solitons constructed by Deruelle under $L^\infty$ perturbation of links. In particular, the $C^0$-convergence of smooth links implies the smooth convergence of the expanding solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-dimensional flying wing Steady Ricci Solitons Chan, Pak-Yeung Lai, Yi Lee, Man-Chun Differential Geometry 53E20 For any $n\geq 4$, we construct an $(n-2)$-parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor at a critical point of the soliton potential. Among them lies an $(n-3)$-parameter subfamily of non-collapsed solitons. These solitons generalized the flying wings constructed by the second named author and produced new examples of steady gradient Ricci solitons with non-negative curvature operator for $n\geq 4$. Our approach is based on constructing continuous families of Ricci flows smoothing emanating from continuous families of spherical polyhedra which still preserves symmetry. This is built upon a new stability result of Ricci flows with scaling invariant estimates. As another application of the method, we prove the stability of asymptotically conical expanding solitons constructed by Deruelle under $L^\infty$ perturbation of links. In particular, the $C^0$-convergence of smooth links implies the smooth convergence of the expanding solitons. |
| title | Higher-dimensional flying wing Steady Ricci Solitons |
| topic | Differential Geometry 53E20 |
| url | https://arxiv.org/abs/2510.23005 |