Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow (Memoirs of the American Mathematical Society)

Stolarski, Maxwell

American Mathematical Society（2024/05発売）

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製本 Paperback:紙装版/ペーパーバック版／ページ数 153 p.
言語 ENG
商品コード 9781470468767
DDC分類 516.362

Full Description

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 x 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.

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