The calculation of the L^sup 2^-norm of the index of a plane curve and related formulas

We provide formulas for calculating the L ^sup 2^-norm of the index function of a rectifiable closed curve in the complex plane. Some applications to isoperimetric inequalities are given. The main tool used is the decomposition of a rectifiable closed curve into a sequence of Jordan curves, curves w...

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Bibliographic Details
Published inJournal d'analyse mathématique (Jerusalem) Vol. 120; no. 1; p. 225
Main Authors Carmona, Joan Josep, Cufí, Julià
Format Journal Article
LanguageEnglish
Published Jerusalem Springer Nature B.V 01.08.2013
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Summary:We provide formulas for calculating the L ^sup 2^-norm of the index function of a rectifiable closed curve in the complex plane. Some applications to isoperimetric inequalities are given. The main tool used is the decomposition of a rectifiable closed curve into a sequence of Jordan curves, curves with null index functions, and an exceptional set.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-013-0019-9