Steiner symmetrization along a certain equidistributed sequence of directions

Published in Arxiv, 2020

Reza Asad , Almut Burchard. Arxiv 2020.

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Abstract

This note reports the results of an undergraduate research project from the year 2013-14, concerning the convergence of iterated Steiner symmetrizations in the plane. The directions of symmetrization are chosen according to the Van der Corput sequence, a classical example of a sequence that is equidistributed in S1 with low discrepancy. It is shown here that the resulting iteration of Steiner symmetrizations converges to the symmetric decreasing rearrangement. The proof exploits the self-similarity of the sequence of angular increments, using the technique of competing symmetries.