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- Title
A characterization of the Euclidean ball via antipodal points.
- Authors
Lu, Xuguang
- Abstract
Arising from an equilibrium state of a Fermi–Dirac particle system at the lowest temperature, a new characterization of the Euclidean ball is proved: a compact set K ⊂ R n (having at least two elements) is an n-dimensional Euclidean ball if and only if for every pair x , y ∈ ∂ K and every σ ∈ S n - 1 , either 1 2 (x + y) + 1 2 | x - y | σ ∈ K or 1 2 (x + y) - 1 2 | x - y | σ ∈ K . As an application, a measure version of this characterization of the Euclidean ball is also proved and thus the previous result proved for n = 3 on the classification of equilibrium states of a Fermi–Dirac particle system holds also true for all n ≥ 2 .
- Subjects
FERMIONS; EUCLIDEAN distance; LOW temperatures; EQUILIBRIUM
- Publication
Aequationes Mathematicae, 2024, Vol 98, Issue 3, p637
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-024-01055-3