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Déformation J-équivalente de polynômes géometriquement finis

Peter Haïssinsky (2000)

Fundamenta Mathematicae

Any geometrically finite polynomial f of degree d ≥ 2 with connected Julia set is accessible by structurally stable sub-hyperbolic polynomials of the same degree. Moreover, they are topologically conjugate to f on their Julia sets.

Déformation localisée de surfaces de Riemann.

Peter Haïssinsky (2005)

Publicacions Matemàtiques

Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T(X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D= T(X) if and only if the components of X Y are all disks or punctured disks.

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