The curvature of level curves

Shaffer, Dorothy Browne

doi:10.1090/S0002-9947-1971-0277695-5

The curvature of level curves
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Trans. Amer. Math. Soc. 158 (1971), 143-150 Request permission

Abstract:

Sharp bounds are derived for the curvature of level curves of analytic functions in the complex plane whose logarithmic derivative has the representation $c/(w - g(w))$, where $g(w)$ is analytic for $|w| > a$ and $|g(w)| \leqq a,c$ real. These results are applied in particular to lemniscates and sharpened for the level curves of lacunary polynomials. Extensions to the level curves of Green’s function and rational functions are indicated.

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