Curvature Blow-Up in Doubly-warped Product Metrics Evolving by Ricci Flow
著者
書誌事項
Curvature Blow-Up in Doubly-warped Product Metrics Evolving by Ricci Flow
（Memoirs of the American Mathematical Society, no. 1470）
American Mathematical Society, c2024
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注記
"March 2024, volume 295, number 1470 (second of 6 numbers)"
Includes bibliographical references (p. 145-147)
内容説明・目次
内容説明
For any manifold Np admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products M = Np × Sq+1 with doubly warped product metrics. In particular, we provide a rigorous construction of local, type II, conical singularity formation on such spaces. It is shown that for any k > 1 there exists a solution with curvature blow-up rateRm ∞ (t) (T ? t)?k with singularity modeled on a Ricci-flat cone at parabolic scales.
目次
Chapters
1. Introduction
2. Setup and preliminaries
3. The initial data and the topological argument
4. Pointwise estimates
5. No inner region blow-up
6. Coefficient estimate
7. Short-time estimates
8. Long-time estimates
9. Scalar curvature behavior
A. Analytic facts
B. Constants
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