Construction of a Dirichlet form on metric measure spaces of controlled geometry

Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam

Given a compact doubling metric measure space $X$ that supports a $2$-Poincaré inequality, we construct a Dirichlet form on $N^{1,2}(X)$ that is comparable to the upper gradient en…