Definition:Staircase Contour

Definition
Let $C$ be a contour that is a concatenation of the directed smooth curves $C_1, \ldots, C_n$.

For all $i \in \left\{ {1, \ldots, n}\right\}$, let it be possible for $C_i$ be parameterized by a smooth path $\gamma_i: \left[{0 \,.\,.\, 1}\right] \to \C$ such that either:


 * $\gamma_i \left({t}\right) = z_i + t r_i$

or


 * $\gamma_i \left({t}\right) = z_i + i t r_i$

for some $z_i \in \C, r_i \in \R$ for all $t \in \left[{0 \,.\,.\, 1}\right]$.

Then $C$ is called a staircase contour.

Illustration

 * [[File:ConnectedDomainStaircase.png]]