The Riemannian structure of John and uniform domains in $\mathbb{R}^n$

Using the theory of pre-ends, we study the boundary and metric properties of John and uniform domains in the Euclidean $n$-space. We obtain some results on the metric Riemannian structure of these classes of domains. We prove that the family of John domains is closed under the class of homeomorphisms quasi-isometric in the intrinsic Riemannian metric and the family of uniform domains is closed under the class of bi-Lipschitz mappings.