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The Strong Mankiewicz Property for Closed Convex Body in Normed Spaces
Abstract
Mori and Ozawa raised a fundamental open question: whether every convex body in a normed space enjoys the strong Mankiewicz property (SMP). The SMP states that every surjective isometry from the convex body onto a convex subset of an arbitrary real normed space is necessarily real-affine, with no interior assumption imposed on the target convex set. In the present work, we settle this problem affirmatively.
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BibTeX
@misc{wang2026strong,
title = {{The Strong Mankiewicz Property for Closed Convex Body in Normed Spaces}},
author = {Ruidong Wang and Jianglong Luo and Li Tang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34113},
eprint = {2610.34113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34113},
}
RIS
TY - UNPB
TI - The Strong Mankiewicz Property for Closed Convex Body in Normed Spaces
AU - Ruidong Wang
AU - Jianglong Luo
AU - Li Tang
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34113
UR - https://arxiv.org/abs/2610.34113
AB - Mori and Ozawa raised a fundamental open question: whether every convex body in a normed space enjoys the strong Mankiewicz property (SMP). The SMP states that every surjective isometry from the convex body onto a convex subset of an arbitrary real normed space is necessarily real-affine, with no interior assumption imposed on the target convex set. In the present work, we settle this problem affirmatively.
ER -