Type II singularities on complete non-compact Yamabe flow

Choi, Beomjun; Daskalopoulos, Panagiota; King, John

Abstract

This work concerns with the existence and detailed asymptotic analysis of Type II singularities for solutions to complete non-compact confor-mally flat Yamabe flow with cylindrical behavior at infinity. We provide the specific blow-up rate of the maximum curvature and show that the solution converges, after blowing-up around the curvature maximum points, to a rota-tionally symmetric steady soliton. It is the first time that the steady soliton is shown to be a finite time singularity model of the Yamabe flow.

Citation

Choi, B., Daskalopoulos, P., & King, J. (2021). Type II singularities on complete non-compact Yamabe flow. Journal für die reine und angewandte Mathematik, 2021(772), 83-119. https://doi.org/10.1515/crelle-2020-0032

• Journal Article Type: Article
• Acceptance Date: Jan 20, 2020
• Online Publication Date: Oct 8, 2020
• Publication Date: 2021
• Deposit Date: Apr 6, 2020
• Publicly Available Date: Oct 9, 2021
• Journal: Journal für die reine und angewandte Mathematik
• Print ISSN: 1435-5345
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 2021
• Issue: 772
• Pages: 83-119
• DOI: https://doi.org/10.1515/crelle-2020-0032
• Public URL: https://nottingham-repository.worktribe.com/output/4155572
• Publisher URL: https://www.degruyter.com/view/journals/crll/ahead-of-print/article-10.1515-crelle-2020-0032/article-10.1515-crelle-2020-0032.xml