Characterizations of generalized John domains in $\mathbb{R}^n$ via metric duality

Abstract

Using the metric duality theory developed by Vaisala, we characterize generalized John domains in terms of higher dimensional homological bounded turning for its complement under mild assumptions. Simple examples indicate that our assumptions for such a characterization are optimal. Furthermore, we show that similar results in terms of higher dimensional homotopic bounded turning do not hold in three dimension.Comment: 24 pages, 17 figures, substantial changes on the introductio