论文标题
关于schrödinger图的全球动力学在谐波图附近双曲机上流动
On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps
论文作者
论文摘要
本文的结果是双重的：在第一部分中，我们证明，对于Schrödinger地图，从双曲机平面到带有非阳性截面曲率的Riemannian表面，谐波图是骨膜或反塑性的谐波图，其较大尺寸的抗塑性是渐近稳定的。在第二部分中，我们证明，对于Schrödinger图，从双曲机平面流向Kähler歧管，小尺寸的可接受的谐波图是渐近稳定的。此处指定的渐近稳定性结果包含两种类型：一种是$ l^{\ iffty} _x $作为先前的作品中的收敛性，另一个是能量空间中的谐波图和辐射项的收敛，这在Schrödinger地图文献中是新的，而无需对称假设。
The results of this paper are twofold: In the first part, we prove that for Schrödinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or anti-holomorphic of arbitrary size are asymptotically stable. In the second part, we prove that for Schrödinger map flows from hyperbolic planes into Kähler manifolds, the admissible harmonic maps of small size are asymptotically stable. The asymptotic stability results stated here contain two types: one is the convergence in $L^{\infty}_x$ as the previous works, the other is convergence to harmonic maps plus radiation terms in the energy space, which is new in literature of Schrödinger map flows without symmetry assumptions.
