Displaying similar documents to “Dirichlet points, Garnett points, and infinite ends of hyperbolic surfaces. I.”

Legendrian dual surfaces in hyperbolic 3-space

Kentaro Saji, Handan Yıldırım (2015)

Annales Polonici Mathematici


We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the...

Riemann surfaces with boundary and natural triangulations of the Teichmüller space

Gabriele Mondello (2011)

Journal of the European Mathematical Society


We compare some natural triangulations of the Teichmüller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell–Wolf’s proof to show that grafting semi-infinite cylinders at the ends of hyperbolic surfaces with fixed boundary lengths is a homeomorphism. This way, we construct a family of equivariant triangulations of the Teichmüller space of punctured surfaces that interpolates between Bowditch–Epstein–Penner’s (using the spine construction)...

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications


In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.