Curvature Blow-Up in Doubly-warped Product Metrics Evolving by Ricci Flow
Author(s)
Bibliographic Information
Curvature Blow-Up in Doubly-warped Product Metrics Evolving by Ricci Flow
（Memoirs of the American Mathematical Society, no. 1470）
American Mathematical Society, c2024
Available at 1 libraries
Note
"March 2024, volume 295, number 1470 (second of 6 numbers)"
Includes bibliographical references (p. 145-147)
Description and Table of Contents
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 × 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.
Table of Contents
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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