Harmonic Maps to Teichmüller Space

Harmonic Maps to Teichmüller Space

We give sufficient conditions for the existence of equivariant harmonic maps from the universal cover of a Riemann surface B to the Teichmüller space of a genus g ≥ 2 surface Σ. The condition is in terms of the representation of the fundamental group of B to the mapping class group of Σ. The metric on Teichmüller space is chosen to be the Kähler hyperbolic metric. Examples of such representatio...

Computing Teichmüller Maps between Polygons

By the Riemann-mapping theorem, one can bijectively map the interior of an n-gon P to that of another n-gon Q conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of P to those Q. In this case, one wants to find the “best" mapping between these polygons, i.e., one that minimizes the maximum angle distortion (the dilatation) over all points in P . ...

Quantum Teichmüller Space

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Dynamics over Teichmüller Space

Fuzzy Subgroups and the Teichmüller Space

There exists a generalization of the Teichmüller space of a covering group. In this paper we combine this generalized Teichmüller space T (G) and any fuzzy subgroup A : G−→ F where G is a subgroup of the group consisting of such orientation preserving and orientation reversing Möbius transformations which act in the upper half-plane of the extended complex plane. A partially ordered set F = (F ...