3 papers
math.MG2026
Validity of the Strong Version of the Union of Uniform Closed Balls Conjecture in the Plane
Chadi Nour, Jean Takche
We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.
math.MG2025
New Characterizations of Strong Convexity
Chadi Nour, Jean Takche
Parallel to the main results of [13] and [14], which explore the equivalence between prox-regularity, the exterior sphere condition, and -convexity, we present novel characteriz…
math.MG2024
The Complement of a Closed Set Satisfying the Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We provide a novel analytical proof of an improved version of [10, Theorem 3.1], showing that the complement of a closed set satisfying the extended exterior sphere condition is no…