arXiv subjects

Harumi Tanigawa

Publications and source records attributed to Harumi Tanigawa.

3 recordsLinked to original sources

arXiv1996

Divergence of projective structures and lengths of measured laminations

Given a complex structure, we investigate diverging sequences of projective structures on the fixed complex structure in terms of Thurston's parametrization. In particular, we will give a geometric proof to the theorem by Kapovich stating that as the projective structures on a fixed complex structure diverge so do their monodromies. In course of arguments, we extend the concept of realization of laminations for PSL$(2,{\mathbf C})$-representations of surface groups.

math.CV↗

arXiv1995

Projective structures with discrete holonomy representations

Let $K(X)$ denote the set of projective structures on a compact Riemann surface $X$ whose holonomy representations are discrete. We will show that each component of the interior of $K(X)$ is holomorphically equivalent to a complex submanifold of the product of Teichmüller spaces and the holonomy representation of every projective structure in the interior of $K(X)$ is a quasifuchsian group.

math.DG↗

arXiv1995

Grafting, harmonic maps, and projective structures on surfaces

Grafting is a surgery on Riemann surfaces introduced by Thurston which connects hyperbolic geometry and the theory of projective structures on surfaces. We will discuss the space of projective structures in terms of the Thurston's geometric parametrization given by grafting. From this approach we will prove that on any compact Riemann surface with genus greater than $1$ there exist infinitely many projective structures with Fuchsian holonomy representations. In course of the proof it will turn out that grafting is closely related to harmonic maps between surfaces.

math.DG↗