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

Name: Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow
Brand: AMERICAN MATHEMATICAL SOCIETY
SKU: 9781470468767
Price: 219.0 AUD
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AMERICAN MATHEMATICAL SOCIETYISBN: 9781470468767

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$219.00

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By Maxwell Stolarski
Imprint: AMERICAN MATHEMATICAL SOCIETY
Release Date: August 29, 2024
Format: PAPERBACK
Pages: 153

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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

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

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