Yamabe流完全非紧解的熄灭轮廓
Extinction profile of complete non-compact solutions to the Yamabe flow
摘要：
本文研究了共形平坦Yamabe流完全非紧解的{ \em奇异性形成}，该流的共形因子具有{ \em无穷远圆柱行为}。它们的奇异性轮廓恰好是{ \em Yamabe孤子}，它是演化度规的保角因子所满足的快扩散方程的{ \em自相似解}.自相似轮廓由初始数据在无穷远处的二阶渐近性确定，该渐近性与相应的自相似解的渐近性相匹配。溶液可能在圆柱形尾部的消亡时$T$熄灭，或者可能比$T$更长。在第一种情况下，奇点分布由{ \em Yamabe收缩器}描述，该收缩器在时间$T$处消失。在第二种情况下，奇异性分布由稍早于$T$的{ \em奇异} Yamabe收缩器和稍晚于$T$的匹配{ \em Yamabe扩展器}描述。
英文摘要：
This work addresses the {\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\em cylindrical behavior at infinity}. Their singularity profiles happen to be {\em Yamabe solitons}, which are {\em self-similar solutions} to the fast diffusion equation satisfied by the conformal factor of the evolving metric. The self-similar profile is determined by the second order asymptotics at infinity of the initial data which is matched with that of the corresponding self-similar solution. Solutions may become extinct at the extinction time $T$ of the cylindrical tail or may live longer than $T$. In the first case the singularity profile is described by a {\em Yamabe shrinker} that becomes extinct at time $T$. In the second case, the singularity profile is described by a {\em singular} Yamabe shrinker slightly before $T$ and by a matching {\em Yamabe expander} slightly after $T$ .
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