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.
|Journal||Journal d'Analyse Mathematique|
|Publication status||Published - 1 Aug 2013|