I think this has something to do with convexity. The shape of this is like a star and is convex. Is this a necessary condition for a ball?Prove that the set $\displaystyle G=\{(x_1,x_2) \ : |x_1|^{\frac{1}{3}}+|x_2|^{\frac{1}{3}} \leq 1 \}$ is not a unit ball in any metric induced by a norm on $\displaystyle \mathbb{R}^2$.