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arXiv · 2103.02478

On lower estimations of square-linear ratio for plane Peano curves

Evgeny Shchepin·Evgeny Mychka
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Abstract

It is proved that for any mapping of a unit segment to a unit square, there is a pair of points of the segment for which the square of the Euclidean distance between their images exceeds the distance between them on the segment by at least $3\frac58$ times. And the additional condition that the images of the beginning and end of the segment belong to opposite sides of the square increases the estimate to $4+\varepsilon$.

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Evgeny Shchepin, Evgeny Mychka. 2021-03-03. On lower estimations of square-linear ratio for plane Peano curves. https://arxiv.org/abs/2103.02478

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