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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The curvature of level curves

Author: Dorothy Browne Shaffer
Journal: Trans. Amer. Math. Soc. 158 (1971), 143-150
MSC: Primary 30.10
MathSciNet review: 0277695
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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 $ \vert w\vert > a$ and $ \vert g(w)\vert \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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Keywords: Level line, lemniscate, curvature, lacunary polynomial, convexity
Article copyright: © Copyright 1971 American Mathematical Society

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