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Steiner symmetrization with respect to the Kakutani-Fibonacci sequence of directions

Ingrid Carbone, Aljoša Volčič

Abstract

In this paper we will prove that for any planar measurable set of finite measure $M$, its successive Steiner symmetrizations with respect to the Kakutani-Fibonacci sequence of directions converge to the ball $M^*$ centered at the origin and having the same measure.

Steiner symmetrization with respect to the Kakutani-Fibonacci sequence of directions

Abstract

In this paper we will prove that for any planar measurable set of finite measure , its successive Steiner symmetrizations with respect to the Kakutani-Fibonacci sequence of directions converge to the ball centered at the origin and having the same measure.
Paper Structure (5 sections, 19 equations)

This paper contains 5 sections, 19 equations.

Table of Contents

  1. Introduction
  2. Basic definitions
  3. Kakutani-Fibonacci sequence
  4. The Kakutani-Fibonacci Steiner process.
  5. Final remarks.