Generalized exterior sphere conditions and $\varphi$-convexity
Chadi Nour, Ron J. Stern, Jean Takche · Discrete and Continuous Dynamical Systems · 2010
We consider sets $S\subset\R^n$ satisfying a certain exterior sphere condition, and it is shown that under wedgedness of $S$, it coincides with $\varphi$-convexity. We also offer related improvements concerning the union of uniform closed balls conjecture.