Title: A blow-up formula for stationary quaternionic maps Show Chinese title

Title: 具有静态四元数映射的爆破公式

Abstract: Let $(M, J^\alpha, \alpha =1,2,3)$ and $(N, {\cal J}^\alpha, \alpha =1,2,3)$ be Hyperk\"ahler manifolds. Suppose that $u_k$ is a sequence of stationary quaternionic maps and converges weakly to $u$ in $H^{1,2}(M,N)$, we derive a blow-up formula for $\lim_{k\to\infty}d(u_k^*{\cal J}^\alpha)$, for $\alpha=1,2,3$, in the weak sense. As a corollary, we show that the maps constructed by Chen-Li [CL2] and by Foscolo [F] can not be tangent maps (c.f [LT], Theorem 3.1) of a stationary quaternionic map satisfing $d(u^*{\cal J}^\alpha)=0$. Show Chinese abstract

Abstract: 设 $(M, J^\alpha, \alpha =1,2,3)$ 和 $(N, {\cal J}^\alpha, \alpha =1,2,3)$ 是超凯勒流形。 假设 $u_k$ 是一个平稳四元数映射序列，并且在 $H^{1,2}(M,N)$ 中弱收敛到 $u$，我们推导出 $\lim_{k\to\infty}d(u_k^*{\cal J}^\alpha)$ 的爆破公式，对于 $\alpha=1,2,3$，在弱意义下。 由此得出推论，我们证明了由Chen-Li [CL2]和Foscolo [F]构造的映射不可能是满足$d(u^*{\cal J}^\alpha)=0$的平稳四元数映射的切映射（参见[LT]，定理3.1）。