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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The curvature of level curves
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by Dorothy Browne Shaffer
Trans. Amer. Math. Soc. 158 (1971), 143-150
DOI: https://doi.org/10.1090/S0002-9947-1971-0277695-5

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.
References
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Bibliographic Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 158 (1971), 143-150
  • MSC: Primary 30.10
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0277695-5
  • MathSciNet review: 0277695