It is already known that bounded harmonic functions defined on Lipschitz bounded domains in Euclidean space are epsilon-approximable. It means that for a bounded harmonic function u and a given epsilon one can find a function of bounded variation such that its distance from u in supremum norm is less than epsilon and the norm of its gradient is a Carleson measure. We will prove that in the setting of Riemannian manifold the same holds. That property is essential in proving Quantitative Fatou Property on Riemannian manifold.
Meeting ID: 851 2259 3154 Passcode: 541535