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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	225-253
Revista	Journal d'Analyse Mathematique
Volum	120
Número	1
DOIs	https://doi.org/10.1007/s11854-013-0019-9
Estat de la publicació	Publicada - 1 d’ag. 2013

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10.1007/s11854-013-0019-9

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title = "The calculation of the L2-norm of the index of a plane curve and related formulas",

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.",

author = "Carmona, {Joan Josep} and Juli{\`a} Cuf{\'i}",

year = "2013",

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doi = "10.1007/s11854-013-0019-9",

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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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DO - 10.1007/s11854-013-0019-9

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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