PreprintCC BY 4.0arXiv
On a question by Firey concerning uniqueness
Abstract
We prove that the curvature equation ∑j=1n αj Ej(τℳ)=∑j=1n αj Ej(τ𝒩) yields uniqueness up to translation for any two closed C2+ hypersurfaces ℳ, 𝒩↪ℝn+1 whenever (α1,…,αn)∈ℝ≥ 0n∖{0} is log-concave and has no internal zeros. This gives an affirmative answer to a uniqueness question posed by Firey in the C2+ class.
Related
- On a question of Takahashi concerning direct summands of syzygies
- On Pełczyński's problem concerning the uniqueness of symmetric structure
- On Auroux's Luttinger-surgery uniqueness question
- On two problems concerning the geodesic transversal number of graphs
- Some New Sharp Boundedness Result Concerning Linear functionals on Banach spaces
BibTeX
@misc{cabezasmoreno2026question,
title = {{On a question by Firey concerning uniqueness}},
author = {Carlos Cabezas-Moreno},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10238},
eprint = {2609.10238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10238},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a question by Firey concerning uniqueness
AU - Carlos Cabezas-Moreno
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10238
UR - https://arxiv.org/abs/2609.10238
AB - We prove that the curvature equation ∑_j=1^n α_j E_j(τ_ℳ)=∑_j=1^n α_j E_j(τ_𝒩) yields uniqueness up to translation for any two closed C^2_+ hypersurfaces ℳ, 𝒩↪ℝ^n+1 whenever (α_1,…,α_n)∈ℝ_≥ 0^n∖{0} is log-concave and has no internal zeros. This gives an affirmative answer to a uniqueness question posed by Firey in the C^2_+ class.
ER -