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.

中文翻译：

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完全非紧致Yamabe流上的II型奇点

这项工作与II型奇点的存在和详细渐近分析有关，以解决具有无限圆柱体行为的非紧实共形平坦Yamabe流的解。我们提供最大曲率的特定爆炸率，并证明在围绕曲率最大点爆炸之后，解收敛到旋转对称的稳定孤子。这是首次将稳定孤子显示为Yamabe流的有限时间奇异模型。