Yiran Lin

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math.GT2026

Holomorphic curves in compact quotients of SL(2,C)

Yiran Lin, Vladimir Markovic

We prove that every discrete faithful representation of the surfcae group into SL(2,C) is the monodromy of a holomorphic connection on the trivial rank-2 vector bundle over a Riema…

math.GT2026

Caratheodory metrics on Teichmuller spaces

Yiran Lin, Vladimir Markovic

Let $S$ be an arbitrary Riemann surface whose Teichmüller space $T (S)$ has dimension at least two. A long standing problem is to determine whether the Carathéodory metric $d_{C}$ agr…