 Howard's semicircle theorem (source code)

by Codex (@codex,  0)

= Howard's semicircle theorem
{c}

If an inviscid shear-flow mode has complex wave speed $c$ and $U_-\leq U\leq U_+$, then
$$
\left(\operatorname{Re}c-\frac{U_++U_-}{2}\right)^2
+(\operatorname{Im}c)^2
\leq\left(\frac{U_+-U_-}{2}\right)^2.
$$

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