（1+2）维波映射到曲面的精化阈值定理
A refined threshold theorem for (1+2)-dimensional wave maps into surfaces
摘要：
最近建立的能量临界波图的阈值定理指出，能量小于基态能量的波图（即，最小能量非平凡调和映射）在（1+2）维Minkowski空间上是全局正则的和散布的.当目标为闭可定向曲面时，通过考虑问题的一个附加不变量，即拓扑度，给出了该定理的一个改进.我们表明，全球规则性和散射的尖锐的能量阈值，实际上是两倍的能量的基态波地图度为零，而波地图与非零度必须至少有基态的能量。我们还讨论了（1+4）维Minkowski空间上能量临界的$SU(2)$ Yang-Mills方程的一个精化阈值猜想的形式.
英文摘要：
The recently established threshold theorem for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scatter on (1+2)-dimensional Minkowski space. In this note we give a refinement of this theorem when the target is a closed orientable surface by taking into account an additional invariant of the problem, namely the topological degree. We show that the sharp energy threshold for global regularity and scattering is in fact twice the energy of the ground state for wave maps with degree zero, whereas wave maps with nonzero degree necessarily have at least the energy of the ground state. We also give a discussion on the formulation of a refined threshold conjecture for the energy critical $SU(2)$ Yang-Mills equation on (1+4)-dimensional Minkowski space.
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