Zalcman space conjecture for complex affine spaces

Let $\mathbb C^n$ denote complex affine $n$-space, and let a Zalcman space be a complex space satisfying the property that every non-normal, non-compactly-divergent family of holomorphic maps from the unit disc admits, after rescaling around points converging in the disc, a subsequence converging uniformly on compact subsets of $\mathbb C$ to a nonconstant holomorphic curve into the space.

Zalcman space conjecture. $\mathbb C^n$ is a Zalcman space for each $n\geq 2$.

As far as the source indicates, this conjecture remains open. The paper studies the conjecture and proves it under additional bounded-derivative hypotheses for limit holomorphic curves.