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

Maxwell Stolarski (Autor)

Buch | Softcover

153 Seiten

2024
American Mathematical Society (Verlag)
978-1-4704-6876-7 (ISBN)

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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 × 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

Erscheinungsdatum	02.05.2024
Reihe/Serie	Memoirs of the American Mathematical Society ; Volume: 295 Number: 1470
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	272 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-6876-X / 147046876X
ISBN-13	978-1-4704-6876-7 / 9781470468767
Zustand	Neuware