As on arXiv
Abstract
For any , we construct an -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 -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 . 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 perturbation of links. In particular, the -convergence of smooth links implies the smooth convergence of the expanding solitons.
Comments: 51 pages, introduction revised. Printing mistakes fixed. Result on stability of expanders added
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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A family of Kähler flying wing steady Ricci solitons
Topics Stability & uniqueness, Ricci solitons · Same authors Pak-Yeung Chan, Yi Lai · Shared terms “wing steady”, “flying wing”, “steady Ricci”
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O(2)-symmetry of 3D steady gradient Ricci solitons
Topics Ricci solitons · Same author Yi Lai · Shared terms “flying wing”, “steady gradient”, “gradient Ricci”
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3D flying wings for any asymptotic cones
Topics Ricci solitons · Same author Yi Lai · Shared terms “flying wing”, “steady gradient”, “gradient Ricci”
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Topics Ricci solitons · Same authors Pak-Yeung Chan, Man-Chun Lee · Shared terms “conical expanding”, “gradient Ricci”, “Deruelle”
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Topics Boundaries & non-compact, Stability & uniqueness, Ricci solitons · Same author Pak-Yeung Chan · Shared terms “expanding solitons”, “curvature operator”, “gradient Ricci”
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Topics (Non)collapsing, Boundaries & non-compact, Stability & uniqueness · Same author Man-Chun Lee · Shared terms “invariant estimate”, “scaling invariant”, “collapsed”
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Expanding Ricci solitons coming out of weakly PIC1 metric cones
Topics Ricci solitons · Same authors Pak-Yeung Chan, Man-Chun Lee · Shared terms “Deruelle”, “gradient Ricci”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 9B.3Collapsing and Noncollapsing
Injectivity radius bounds from volume, collapsing examples, and the definition Perelman needs.
- 12A.4κ-Noncollapsing
The theorem that excludes the cigar.
- 12A.8Local Noncollapsing from the Reduced Volume
Perelman's §§7.3 and 8: noncollapsing that needs only local curvature control, the small-and-large-vector split, the maximum principle for the reduced distance, and the form that survives surgery.