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              <p>Abstract We show that on convex domains with $$\mathcal {C}^{1,\alpha }$$ C 1 , α -smooth boundary the limit set of non-visible Kobayashi geodesics are contained in a complex face. In $$\mathbb {C}^2$$ 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 ( $$\mathbb {C}$$ C -)convex domains whose boundary contains a complex tangential line segment of non-Goldilocks points in a specific direction.</p>
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