A blow-up formula for stationary quaternionic maps

Let ( M, J α , α = 1 , 2 , 3) and ( N, J α , α = 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 →∞ d ( u ∗ k J α ), for α = 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 ∗ J α ) = 0.