We study conformal metrics on the unit ball of Euclidean space. We prove an extension of a theorem originally due to Gerasch on the broadly accessibility of the boundary points of a domain quasiconformally equivalent to a ball. We also show that our result is close to optimal. Our abstract approach leads to new results also for the boundary behavior of (quasi)conformal mappings.
"Conformal metrics and boundary accessibility." Illinois J. Math. 53 (1) 25 - 38, Spring 2009. https://doi.org/10.1215/ijm/1264170837