The calculation of the L 2-norm of the index of a plane curve and related formulas |
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| Authors: | Joan Josep Carmona Julià Cufí |
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| Affiliation: | 1. Departament de Matemàtiques Edifici C, Universitat Aut?noma de Barcelona, 08193, Bellaterra-Barcelona, Catalunya
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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. |
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