Let $D$ be a bounded convex domain in $\mathbb R^2$, if $\xi\in\partial D$ is it true that, there exists an $R>0$ and a convex function $\gamma:\mathbb R\to \mathbb R$ such that upto suitable choice of coordinates we have $$D\cap B(\xi,R):= \{\ (x,y)\in B(\xi,R)\ :\ y>\gamma(x)\ \}?$$ And for strictly convex domain we can we choose this function to be strictly convex ?
Suggestions for some helpful references related to this will be highly appreciated.
