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In degenerating surface, Robert Bryant give us an example of a sequence of minimal immersions which converges (in $C^2$- topology) to $z\mapsto z^{2k+1}$ on the unit disc $\mathbb{D}$. My question is ...

Hi, i have a sequence of immersed disc $u_n: \mathbb{D} \rightarrow \mathbb{R}^3$ which converge to a singular cover of the disc: $z^k$ for $k\geq 2$, moreprecisely $u_n \rightarrow z^k$ in $C^2(\...