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9781470468767 Academic Inspection Copy

Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow

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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.
Maxwell Stolarski, Arizona State University, Tempe, AZ.
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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