As on arXiv
Abstract
The goal of this article is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain pde estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian.
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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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Backward propagation of warped product structures and asymptotically conical shrinkers
Topics Rotational symmetry & warped products, Einstein metrics, Boundaries & non-compact
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Local structure of gradient almost Ricci solitons with harmonic Weyl tensor
Topics Eigenvalues & spectrum, Rotational symmetry & warped products, Ricci solitons · Same author Valter Borges · Shared terms “Einstein”
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Rigidity of spherical product Ricci solitons
Topics Einstein metrics, Stability & uniqueness, Ricci solitons · Shared terms “product ricci”
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A note on gradient Ricci soliton warped metrics
Topics Rotational symmetry & warped products, Ricci solitons · Shared terms “nonexistence”, “gradient Ricci”
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The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
Topics Eigenvalues & spectrum, Ricci solitons · Same author Valter Borges · Shared terms “gradient Ricci”
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On the geometry of Riemannian warped product maps
Topics Rotational symmetry & warped products, Ricci solitons
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Geometric properties of second Ricci solitons
Topics Rotational symmetry & warped products, Ricci solitons
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Quasi-Einstein Metrics and a curvature identity associated with the Ricci flow
Topics Rotational symmetry & warped products, Einstein metrics, Stability & uniqueness · Shared terms “gradient Ricci”
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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
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.