论文标题
存在（自旋）表面的（dirac-）谐波图的存在
Existence of (Dirac-)harmonic Maps from Degenerating (Spin) Surfaces
论文作者
论文摘要
我们通过麻袋和乌伦贝克方案研究了从退化表面到非阳性弯曲歧管的谐波图和狄拉克谐波图的存在。通过选择合适的$α$ - （dirac-）谐波图的合适序列，从一系列合适的闭合表面退化为双曲线表面，我们获得了收敛性和在均匀边界能量假设下的清洁能量身份。在这种能量身份中，穿刺附近没有能量损失。作为一种应用，我们从退化（自旋）表面（dirac-）谐波图获得了一个存在结果。如果地图部分的能量也远离零（这是必要条件），则限制谐波映射和狄拉克谐波地图都不平淡。
We study the existence of harmonic maps and Dirac-harmonic maps from degenerating surfaces to non-positive curved manifold via the scheme of Sacks and Uhlenbeck. By choosing a suitable sequence of $α$-(Dirac-)harmonic maps from a sequence of suitable closed surfaces degenerating to a hyperbolic surface, we get the convergence and a cleaner energy identity under the uniformly bounded energy assumption. In this energy identity, there is no energy loss near the punctures. As an application, we obtain an existence result about (Dirac-)harmonic maps from degenerating (spin) surfaces. If the energies of the map parts also stay away from zero, which is a necessary condition, both the limiting harmonic map and Dirac-harmonic map are nontrivial.
