Is every strictly convex, 1-homogeneous function on $\mathbb R^d$ simply a multiple of the Euclidean norm?
Update: The above is no, since any p-norm on $\mathbb R^d$ is strictly convex and 1-homogeneous.
My new question is: Given a norm on $\mathbb R^d$ that is strictly convex, is there any way of characterizing it in relation to known norms? I.e. It's true if and only if the norm is a p-norm for $1< p <\infty$.