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