On Non-visibility of Kobayashi Geodesics and the Geometry of the Boundary.

We show that on convex domains with C 1 , α -smooth boundary the limit set of non-visible Kobayashi geodesics are contained in a complex face. In C 2 this implies the existence of a complex tangential line segment of non-Goldilocks point in the boundary. Conversely, we construct sequences of non-visible almost-geodesics on (C -)convex domains whose boundary contains a complex tangential line segment of non-Goldilocks points in a specific direction. [ABSTRACT FROM AUTHOR]