Can we systematically design functions $f(z)$, so that:
$$\left\|\int_{z_0}^{z_{n+1}} f(z)dz\right\|$$
Is guaranteed to be minimal if we pass each of the points $z_1,\cdots,z_n$ along the curve of integration from alternating "sides" like in slalom?
I would imagining it would be possible by placing poles at the specific points and tuning their amplitude somehow but it was ages ago I took analysis in one complex variable.