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math.CV2025
The affine geometry of meromorphic connections with irregular singularities
Xavier Buff, Arnaud Chéritat, Guillaume Tahar
A meromorphic connection on the tangent bundle of a Riemann surface induces a complex affine structure on the complement of the poles. Local models for Fuchsian singularities are a…
math.CV2022
Similarity surfaces, connections, and the measurable Riemann mapping theorem
Arnaud Chéritat, Guillaume Tahar
This article studies a particular process that approximates solutions of the Beltrami equation (straightening of ellipse fields, a.k.a. measurable Riemann mapping theorem) on $\mat…
math.CV2022★ 3 cited
K-differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
We study the local invariants that a meromorphic -differential on a Riemann surface of genus can have for . These local invariants include the orders of zer…