Length functions of lemniscates

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We study metric and analytic properties of generalized lemniscates E_t(f)={z:ln|f(z)|=t}, where f is an analytic function. Our main result states that the length function |E_t(f)| is a bilateral Laplace transform of a certain positive measure. In particular, the function ln|E_t(f)| is convex on any interval free of critical points of ln|f|. As another application we deduce explicit formulas of the length function in some special cases.
18 pages

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Complex Variables, Differential Geometry, 30E05; 42A82; 44A10

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http://salesiana.dossiersoluciones.com/handle/123456789/221688

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306327
 http://arxiv.org/abs/math/0306327
 Manuscr. Math., 112(2003), no 4, 519-538
 doi:10.1007/s00229-003-0411-3

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arXiv