Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1971-0277695-5
MathSciNet review: 0277695
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30.10

Retrieve articles in all journals with MSC: 30.10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0277695-5
Keywords: Level line, lemniscate, curvature, lacunary polynomial, convexity
Article copyright: © Copyright 1971 American Mathematical Society