Type II singularities on complete non-compact Yamabe flow-Reference-Cited by-同舟云学术

Type II singularities on complete non-compact Yamabe flow

Published:2020-10-08 Issue:772 Volume:2021 Page:83-119
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Choi Beomjun¹,Daskalopoulos Panagiota²,King John³

Affiliation:

1. Department of Mathematics , University of Toronto , 40 St George Street , Toronto , ON M5S 2E4 , Canada

2. Department of Mathematics , Columbia University , 2990 Broadway , New York , NY 10027 , USA

3. School of Mathematical Sciences , The University of Nottingham , University Park , Nottingham , NG7 2RD , United Kingdom

Abstract

Abstract This work concerns with the existence and detailed asymptotic analysis of type II singularities for solutions to complete non-compact conformally 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 rotationally 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.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2020-0032/pdf

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