In "Foundations of $p$-adic Teichmüller theory", Mochizuki describes a theory one of whose goals (according to the author) is to generalize Fuchsian uniformization of Riemann surfaces to the $p$-adic context. A quick glance through this book reveals a lot of new concepts (with fancy names!) introduced by Mochizuki.
The question is: what are some landmark papers in this theory (after this textbook)? Did anybody other than Mochizuki and his postdocs/students make contributions to this theory? A less mathematical question: are there any people in Western Europe/U.S. working on this topic in the present?
For example, while I think that Jakob Stix is doing some anabelian geometry (and Mochizuki has made major contributions to it), I am not sure if any of his work is specifically building upon "Foundations of $p$-adic Teichmüller theory".
P.S. Not being an inter-universalist, I do not know whether "Foundations of $p$-adic Teichmüller theory" have anything to do with the IUT. The question, however, is not about IUT. To avoid off-topic debate, let us pretend in this thread that IUT papers do not exist.
Best Answer
From MathSciNet:
MR3905130 Lan, Guitang ; Sheng, Mao ; Yang, Yanhong ; Zuo, Kang . Uniformization of p-adic curves via Higgs–de Rham flows. J. Reine Angew. Math. 747 (2019), 63--108.
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