As on arXiv
Abstract
We show -bounds of the Riemann curvature tensor on a smooth closed -dimensional Ricci flow. To achieve this we introduce the notion of a neck of maximal symmetry, similar to the one in Cheeger-Jiang-Naber and Jiang-Naber and establish a decomposition result by balls with uniform curvature bounds that satisfy an appropriate -content estimate.
Comments: 34 pages. Comments are welcome
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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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Diameter bounds in 3d Type I Ricci flows
Topics Singularities · Same author Panagiotis Gianniotis · Shared terms “Jiang Naber”, “Cheeger Jiang”
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Splitting maps in Type I Ricci flows
Topics Singularities · Same author Panagiotis Gianniotis · Shared terms “Jiang Naber”, “Cheeger Jiang”, “curvature bounds”
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Curvature Bounds on Ricci flows with bounded scalar curvature up to dimension 7
Topics Ricci flow · Shared terms “curvature bounds”, “Jiang”, “Naber”
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A -Hilbert functional in -geometry
Topics Ricci flow · Same author Panagiotis Gianniotis
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Complete -dimensional Ricci flow spacetimes
Topics Singularities · Shared terms “dimensional Ricci”
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Topics Singularities · Shared terms “curvature bounds”
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Higher-order Ricci estimates along immortal Kähler-Ricci flows
Topics Singularities · Shared terms “Riemann curvature”, “curvature bounds”
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Finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
Topics Singularities · Shared terms “curvature bounds”
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
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.