Let $M$ and $N$ be connected and orientable, closed surfaces. For a stable map $\varphi : M \rightarrow N$, denote by $c(\varphi)$ and $n(\varphi)$ the numbers of cusps and nodes of $\varphi$ respectively. In this paper, we determine the minimal number $c(\varphi) + n(\varphi)$ among the apparent contours of degree $d$ stable maps $M \rightarrow N$ whose singular points set consists of one component.
"Apparent contours of stable maps between closed surfaces." Kodai Math. J. 40 (2) 358 - 378, June 2017. https://doi.org/10.2996/kmj/1499846602