几乎极小圆柱边界气泡的分析
Analysis of boundary bubbles for almost minimal cylinders
摘要：
我们分析的Teichmüller调和映射流的解决方案的渐近行为从气缸，更一般的“几乎最小的气缸”，在地图满足高原边界条件的三点条件退化的情况下。我们证明，这样一个退化的边界条件迫使域伸展作为一个边界气泡的形式。我们的主要结果，然后建立，规定的边界曲线，满足道格拉斯的分离条件，这些边界泡将不仅是谐波，但将自己的分支最小浸入。与以前的工作一起，这特别完成了Teichmüller调和映射流将$\mathbb{R}^n$中的每个初始曲面跨越这样的边界曲线变成相应的道格拉斯-高原问题的解的证明。
英文摘要：
We analyse the asymptotic behaviour of solutions of the Teichmüller harmonic map flow from cylinders, and more generally of `almost minimal cylinders', in situations where the maps satisfy a Plateau-boundary condition for which the three-point condition degenerates. We prove that such a degenerating boundary condition forces the domain to stretch out as a boundary bubble forms. Our main result then establishes that for prescribed boundary curves that satisfy Douglas' separation condition, these boundary bubbles will not only be harmonic but will themselves be branched minimal immersions. Together with earlier work, this in particular completes the proof that the Teichmüller harmonic map flow changes every initial surface in $\mathbb{R}^n$ spanning such boundary curves into a solution of the corresponding Douglas-Plateau problem.
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