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math.CV2015★ 9 cited
The holomorphic couch theorem
Maxime Fortier Bourque
We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show tha…
math.CV2014★ 1 cited
The converse of the Schwarz Lemma is false
Maxime Fortier Bourque
Let be a homeomorphism between hyperbolic surfaces with finite topology. If is homotopic to a holomorphic map, then every closed geodesic in is at least as long…
math.CV2013
Finitely connected domains, Rational maps and Ahlfors functions
Maxime Fortier Bourque, Malik Younsi
Using Ahlfors functions, Grunsky maps and the Bell representation theorem, we show that a certain subset of the rational maps of degree forms a trivial bundle over the moduli s…