PreprintCC BY-SA 4.0arXiv
On the Reverse Projection Inequality
Abstract
In \cite {ChenFengLiXiXu2026}, a reverse projection inequality for general convex bodies was established in three dimensions. In this paper, we completely characterize the equality cases of this inequality. We further show that the reverse projection inequality fails in every dimension n≥9. The counterexamples are constructed as full-dimensional polytopes with at most n+2 facets.
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BibTeX
@misc{feng2026reverse,
title = {{On the Reverse Projection Inequality}},
author = {Yibin Feng and Shengnan Hu and Weiru Liu and Lei Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13953},
eprint = {2610.13953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13953},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - On the Reverse Projection Inequality
AU - Yibin Feng
AU - Shengnan Hu
AU - Weiru Liu
AU - Lei Xu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.13953
UR - https://arxiv.org/abs/2610.13953
AB - In \cite {ChenFengLiXiXu2026}, a reverse projection inequality for general convex bodies was established in three dimensions. In this paper, we completely characterize the equality cases of this inequality. We further show that the reverse projection inequality fails in every dimension n≥9. The counterexamples are constructed as full-dimensional polytopes with at most n+2 facets.
ER -