Winding behaviour of finite-time singularities of the harmonic map heat flow*
Winding behaviour of finite-time singularities of the harmonic map heat flow*
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DOI：
10.1007/s00209-003-0582-3
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发表时间：
2004-02
影响因子：
0.8
通讯作者：
P. Topping
中科院分区：
文献类型：
--
作者：
P. Topping
我们解决了有关有限时间奇点处谐波映射热流可能行为的许多问题。特别是，我们证明了气泡的一种非唯一性可以在有限时间发生，我们证明奇异时间流动的弱极限可以是不连续的，我们在一个特定示例中精确确定（多项式）爆炸率，并且我们证明当流动（局部）提升到目标流形的通用覆盖时，流动的“缠绕”行为可能导致意外的收敛失败。
We settle a number of questions about the possible behaviour of the harmonic map heat flow at finite-time singularities. In particular, we show that a type of nonuniqueness of bubbles can occur at finite time, we show that the weak limit of the flow at the singular time can be discontinuous, we determine exactly the (polynomial) rate of blow-up in one particular example, and we show that ‘winding’ behaviour of the flow can lead to an unexpected failure of convergence when the flow is (locally) lifted to the universal cover of the target manifold.