2012/08/21 by Sigurd Angenent, Sigurd B. Angenent, James Isenberg +4
Mathematics · Physics and Astronomy · #53C44 (primary) and 35K59 (secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #gr-qc #math.DG #msc:35K59 #msc:53C44
paper · pdf · doi:10.48550/arxiv.1208.4312
arxiv created 2012/08/21 · openalex publication_date 2012/08/21 · arxiv updated 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In earlier work, we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive integer k≥3, there exist compact solutions in all dimensions m≥3 that become singular at the rate (T-t)-2+2/k.