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

2019/04/30 by Stolarski, Maxwell · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.00087

Abstract

For any manifold N^p admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products M = N^p × S^q+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) \gtrsim (T-t)^-k with singularity modeled on a Ricci-flat cone at parabolic scales.

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