Length functions of lemniscates
classification
🧮 math.CV
math.DG
keywords
functionlengthanalyticlemniscatesanotherapplicationbilateralcases
read the original abstract
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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.