  We study reflected diffusion on uniform domains where the underlying space
admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates.
A celebrated theorem of Jones (Acta Math. 1981) states that uniform domains in
Euclidean space are extension domains for Sobolev spaces. In this work, we
obtain a similar extension property for metric spaces equipped with a Dirichlet
form whose heat kernel satisfies a sub-Gaussian estimate. We introduce a
scale-invariant version of this extension property and apply it to show that
the reflected diffusion process on such a uniform domain inherits various
properties from the ambient space, such as Harnack inequalities, cutoff energy
inequality, and sub-Gaussian heat kernel bounds. In particular, our work
extends Neumann heat kernel estimates of Gyrya and Saloff-Coste (Ast\'erisque
2011) beyond the Gaussian space-time scaling. Furthermore, our estimates on the
extension operator imply that the energy measure of the boundary of a uniform
domain is always zero. This property of the energy measure is a broad
generalization of Hino's result (PTRF 2013) that proves the vanishing of the
energy measure on the outer square boundary of the standard Sierpi\'nski carpet
equipped with the self-similar Dirichlet form.
