论文标题
两泡波图的独特性
Uniqueness of two-bubble wave maps
论文作者
论文摘要
这是两纸系列的第二部分，该系列建立了不会在两个时间方向上散布的阈值能量波图的独特性和规律性。 考虑在1+2尺寸的Minkowski空间上的两球有价值的量大波映射方程，具有等效性k> 3。众所周知，每个拓扑上的琐事波映射，其能量在两个时间方向上都小于唯一的k- equivariant和式谐波Q散布的唯一k-Equivariant谐波Q散布。我们精确地研究了阈值能量的地图，即Q的能量的两倍。 在该系列的第一部分中，我们给出了一个阈值波图的精致构造，该阈值波图将两个谐波图（气泡）的叠加分解为叠加，其中之一是集中在尺度上。在本文中，我们表明该解决方案是唯一的（达到方程式的自然不向导）两个泡沫图。结合我们较早的工作，我们现在可以对每个阈值波映射进行精确描述。
This is the second part of a two-paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider the two-sphere valued equivariant energy critical wave maps equation on 1+2 dimensional Minkowski space, with equivariance class k > 3. It is known that every topologically trivial wave map with energy less than twice that of the unique k-equivariant harmonic map Q scatters in both time directions. We study maps with precisely the threshold energy, i.e., twice the energy of Q. In the first part of the series we gave a refined construction of a threshold wave map that asymptotically decouples into a superposition of two harmonic maps (bubbles), one of which is concentrating in scale. In this paper, we show that this solution is the unique (up to the natural invariances of the equation) two-bubble wave map. Combined with our earlier work we can now give an exact description of every threshold wave map.
