On surfaces, that fill the space

The article is devoted to the construction of dimension-raising maps of cubes with the highest possible Holder exponent. In particular, a square-to-cube mapping with a Holder exponent of $2/3$ is constructed, which is a solution to the V.I.Arnold problem.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.36766
Primary Topic
Mathematical Dynamics and Fractals
Type
preprint
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preprint

On surfaces, that fill the space

E. V. Shchepin
arXiv (Cornell University)
Mathematical Dynamics and Fractals
preprint

On surfaces, that fill the space

E. V. Shchepin
preprint en

Abstract

The article is devoted to the construction of dimension-raising maps of cubes with the highest possible Holder exponent. In particular, a square-to-cube mapping with a Holder exponent of $2/3$ is constructed, which is a solution to the V.I.Arnold problem.

arXiv (Cornell University)
Mathematical Dynamics and Fractals
DOIOpen Access PDFOpenAlex
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On surfaces, that fill the space — E. V. Shchepin · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS