论文标题
带有常规节点的表面谐波图的紧凑性
Compactness of harmonic maps of surfaces with regular nodes
论文作者
论文摘要
在本文中，我们使用Deligne-Mumford Moduli空间和曲线家族制定并证明了谐波图的一般紧凑定理。主定理表明，给定一系列复杂曲线的谐波图，有一个曲线和一个子序列，使得域和地图都从“非规范”节点汇聚在一起。这为颈部零能量和零长度提供了足够的条件。作为推论，可以证明以下已知的事实：如果所有域都差异为$ s^2 $，则能量身份和零距离冒泡。
In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex curves, there is a family of curves and a subsequence such that both the domains and the maps converge off the set of "non-regular" nodes. This provides a sufficient condition for a neck having zero energy and zero length. As a corollary, the following known fact can be proved: If all domains are diffeomorphic to $S^2$, both energy identity and zero distance bubbling hold.
