Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient

Panu Lahti, Lukas Maly, Nageswari Shanmugalingam +1

We study the geometry of domains in complete metric measure spaces equipped with a doubling measure supporting a $1$-Poincaré inequality. We propose a notion of \emph{domain with b…