5 papers · 1 filter
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.
Spherically Supported Property and the Exterior Sphere Condition with Infinite Radius
Chadi Nour
We present several new characterizations of the spherically supported geometric property introduced in [19], emphasizing its connection with the exterior sphere condition with infi…
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…
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…
The Variable Radius Form of the Extended Exterior Sphere Condition
Chadi Nour, Jean Takche
We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothin…