Year: 2026
Type: preprint
Abstract: We prove that the curvature equation $\sum_{j=1}^n α_j E_j(τ_{\mathcal{M}})=\sum_{j=1}^n α_j E_j(τ_{\mathcal{N}})$ yields uniqueness up to translation for any two closed $C^2_+$ hypersurfaces $\mathcal{M}, \mathcal{N}\hookrightarrow\mathbb{R}^{n+1}$ whenever $(α_1,\ldots,α_n)\in\mathbb{R}_{\geq 0}^n\setminus\{0\}$ 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.
Source: arXiv (Cornell University)
Author: Cabezas-Moreno, Carlos
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W7212195132
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