This research demonstrates that sticky Teichmüller geodesics relate to the curve complex distance, refuting a notable conjecture.
We prove that a Teichmüller geodesic with curve endpoints is sticky in the Thurston compactification if and only if the curve complex-distance between the two curve endpoints is at least five. In particular, there exist non-sticky Teichmüller geodesics, which gives a negative answer to Duchin-Fisher’s conjecture.
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Yaozhong Shi (2025) studied this question.
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