In the notation above, suppose that $a>0$ and $b,c,x\in\mathbin{\mathbb{R}}$ with $u_{a,b}(x,0)=0$. Then

$$D=\bigl\{(z_{1},0,x+ic):z_{1}\in\mathbin{\mathbb{C}},\quad|z_{1}|^{2}\leqslant a\bigr\}$$

(58)

is a holomorphic disc in $\mathbin{\mathbb{C}}^{3}$ with boundary in $N_{a,b,c}$, and

$$D^{\prime}=\bigl\{(0,z_{2},x+ic):z_{2}\in\mathbin{\mathbb{C}},\quad|z_{2}|^{2}\leqslant a\bigr\}$$

(59)

is a holomorphic disc in $\mathbin{\mathbb{C}}^{3}$ with boundary in $N_{-a,b,c}$. Furthermore, all holomorphic discs in $\mathbin{\mathbb{C}}^{3}$ with boundary in $N_{\pm a,b,c}$ and invariant under the $\mathbin{\rm U}(1)$-action (52) are of this form.