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

Download or read book Curvature Blow-up in Doubly-warped Product Metrics Evolving by Ricci Flow written by Maxwell Stolarski and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 rate ∥Rm∥∞(t)≥(T-t)-k with singularity modeled on a Ricci-flat cone at parabolic scales.