| Abstract: |
| We consider the equivariant Schr\odinger map from $\mathbb{H}^2$ to $\mathbb{S}^2$ which converges to the north pole of $\mathbb{S}^2$ at the origin and spatial infinity of the hyperbolic space. If the energy of the data is less than $4\pi$, we show that the local existence of Schr\{o}dinger map. Furthermore, if the energy of the data sufficiently small, we prove the solutions are global in time. This is based on joint work with Jiaxi Huang. |
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