PreprintarXiv licencearXiv
Alexandrov Regions
Abstract
We introduce the notion of Alexandrov region. In contrast to Alexandrov spaces these are intrinsic metric spaces, which satisfy a lower curvature bound and have finite Hausdorff dimension, might however, be non-complete. We show a quantitative version of the statement that such regions are locally isometric to an Alexandrov space.
Related
BibTeX
@misc{lebedeva2026alexandrov,
title = {{Alexandrov Regions}},
author = {Nina Lebedeva and Artem Nepechiy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36973},
eprint = {2609.36973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36973},
}
RIS
TY - UNPB
TI - Alexandrov Regions
AU - Nina Lebedeva
AU - Artem Nepechiy
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36973
UR - https://arxiv.org/abs/2609.36973
AB - We introduce the notion of Alexandrov region. In contrast to Alexandrov spaces these are intrinsic metric spaces, which satisfy a lower curvature bound and have finite Hausdorff dimension, might however, be non-complete. We show a quantitative version of the statement that such regions are locally isometric to an Alexandrov space.
ER -