论文标题
沿特定等分的方向序列的施泰纳对称性
Steiner symmetrization along a certain equidistributed sequence of directions
论文作者
论文摘要
本说明报告了2013 - 14年度本科生研究项目的结果，涉及飞机上迭代的施泰纳对称性的融合。根据Van der corput序列选择对称的方向，这是一个序列的经典示例，该序列的经典示例是在低差异上等于在单位圆上的。这里显示的是，施泰纳对称性的产生迭代会收敛于对称减小的重排。证明使用竞争对称性技术利用了角度增量序列的自相似性。
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 on the unit circle 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.
