PreprintCC BY 4.0arXiv
On surfaces, that fill the space
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.
Related
- Tremors and horocycle dynamics on the moduli space of transition surfaces
- Hamiltonian stationary Lagrangian surfaces of constant Gaussian curvature in complex space forms
- Hierarchical hyperbolicity, ball quotients, and the moduli space of smooth cubic surfaces
- Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
- Space-filling surfaces: sharp Hölder continuous parameterizations from squares to cubes
BibTeX
@misc{shchepin2026surfaces,
title = {{On surfaces, that fill the space}},
author = {E. V. Shchepin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36766},
eprint = {2610.36766},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36766},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On surfaces, that fill the space
AU - E. V. Shchepin
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36766
UR - https://arxiv.org/abs/2610.36766
AB - 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.
ER -