  In the last decade, G. Bharali and A. Zimmer defined a class of domains
called Goldilocks domains and they showed that such a domain satisfies a
visibility condition with respect to the Kobayashi extremal curves. Inspired by
their construction, we define a subclass of Goldilocks domains called strongly
Goldilocks domains and we prove a quantitative visibility result on strongly
Goldilocks domains. Using our quantitative visibility result, we extend the
Gehring-Hayman theorem on simply connected planar domains to strongly
Goldilocks domains. As an application of our construction, we also give lower
estimates to the Kobayashi distance.
