Flatness implies Smoothness

Consider an unbounded Reifenberg flat chord arc domain \(D\) in \(\mathbb{R}^{n+1}\) which is a domain with certain flatness conditions, and if the gradient of the Green's function with pole at infinity is bounded above by \(1\) and its normal derivative at the boundary is bounded below by \(1\), then \(D\) is a half space. In this talk, I'll introduce what is a Reifenberg flat chord arc domain and outline sketch of the proof.