PSEUDO-JORDAN DOMAINS AND REFLECTING BROWNIAN MOTIONS

The manifold metric between two points in a planar domain is the minimum of the lengths of piecewise C1 curves in the domain connecting these two points. We define a bounded simply connected planar region to be a pseudo Jordan domain if its boundary under the manifold metric is topologically homeomorphic to the unit circle. It is shown that reflecting Brownian motion X on a pseudo Jordan domain can be constructed starting at all points except those in a boundary subset of capacity zero. X has the expected Skorokhod decomposition under a condition which is satisfied when partial derivative G has finite 1-dimensional lower Minkowski content.