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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The research of both authors was partially supported by the grants MTM2008-05561-C02-02 of the Ministerio de Ciencia e Innovación, Spain and 2009 SGR 1303 of the Generalitat de Catalunya.
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Carmona, J.J., Cufí, J. The calculation of the L 2-norm of the index of a plane curve and related formulas. JAMA 120, 225–253 (2013). https://doi.org/10.1007/s11854-013-0019-9
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DOI: https://doi.org/10.1007/s11854-013-0019-9