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Teichmüller space of a closed set in the Riemann sphere
Xinlong Dong, Arshiya Farhath. G, Sudeb Mitra
The Teichmüller space of a closed set in the Riemann sphere is a simply connected complex Banach manifold. Its complex structure follows from Lieb isomorphism. In this paper, we sh…
On the derivatives of the Liouville currents
Xinlong Dong, Dragomir Šarić, Zhe Wang
The Liouville map, introduced by Bonahon, assigns to each point in the Teichmüller space a natural Radon measure on the space of geodesics of the base surface. The Liouville map is…
Carathéodory metric on some generalized Teichmüller spaces
Xinlong Dong, Sudeb Mitra
We study the Carathéodory metric on some generalized Teichmüller spaces. Earle showed that the Carathéodory metric is complete on any Teichmüller space. Miyachi extended this resul…
Divergent geodesics in the Universal Teichmüller space
Xinlong Dong, Hrant Hakobyan
Thurston boundary of the universal Teichmüller space is the space of projective bounded measured laminations of . A geodesic ray…