PreprintCC BY 4.0arXiv
The Discrete Lp Minkowski Problem for Negative p
Abstract
In this paper, we establish a homological existence criterion for the discrete Lp Minkowski problem for all p<0, where p=−n corresponds to the celebrated centro-affine case. For discrete measures with antipodal support, we obtain a complete existence characterization for arbitrary positive masses. In the even case, a solution can be chosen origin-symmetric.
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BibTeX
@misc{shan2026discrete,
title = {{The Discrete $L_p$ Minkowski Problem for Negative $p$}},
author = {Junjie Shan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01429},
eprint = {2609.01429},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01429},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Discrete L_p Minkowski Problem for Negative p
AU - Junjie Shan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01429
UR - https://arxiv.org/abs/2609.01429
AB - In this paper, we establish a homological existence criterion for the discrete L_p Minkowski problem for all p<0, where p=−n corresponds to the celebrated centro-affine case. For discrete measures with antipodal support, we obtain a complete existence characterization for arbitrary positive masses. In the even case, a solution can be chosen origin-symmetric.
ER -