A countable set of directions is sufficient for Steiner symmetrization
Gabriele Bianchi, Daniel A. Klain, Erwin Lutwak, Deane Yang, and, Gaoyong Zhang
TL;DR
This paper establishes that a countable dense set of directions can be used for Steiner symmetrization, but emphasizes that the sequence order of these directions influences the outcome.
Contribution
It demonstrates that a countable dense set of directions suffices for Steiner symmetrization, highlighting the importance of direction order.
Findings
A countable dense set of directions is sufficient for Steiner symmetrization.
The order of directions significantly affects the symmetrization process.
Direction density alone does not guarantee a unique symmetrization outcome.
Abstract
A countable dense set of directions is sufficient for Steiner symmetrization, but the order of directions matters.
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Taxonomy
TopicsPoint processes and geometric inequalities · Diffusion and Search Dynamics · Morphological variations and asymmetry