The calculation of the L2-norm of the index of a plane curve and related formulas

Joan Josep Carmona; Julià Cufí

doi:10.1007/s11854-013-0019-9

The calculation of the L²-norm of the index of a plane curve and related formulas

Joan Josep Carmona, Julià Cufí

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We provide formulas for calculating the L 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. © 2013 Hebrew University Magnes Press.

Original language	English
Pages (from-to)	225-253
Journal	Journal d'Analyse Mathematique
Volume	120
Issue number	1
DOIs	https://doi.org/10.1007/s11854-013-0019-9
Publication status	Published - 1 Aug 2013

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10.1007/s11854-013-0019-9

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abstract = "We provide formulas for calculating the L 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. {\textcopyright} 2013 Hebrew University Magnes Press.",

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AB - We provide formulas for calculating the L 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. © 2013 Hebrew University Magnes Press.

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The calculation of the L2-norm of the index of a plane curve and related formulas

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The calculation of the L²-norm of the index of a plane curve and related formulas