Maximal surfaces and the universal Teichmüller space

On the Tangent Space to the Universal Teichmüller Space Subhashis Nag

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichmüller Space : (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The complex-analytic model comprising 1-parameter families of schlicht functions on the exterior of the unit disc which allow quasiconformal extension. Indeed, the Fourier...

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.

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 ...

Dynamics over Teichmüller Space

Numerical Computation of Weil-Peterson Geodesics in the Universal Teichmüller Space

We propose an optimization algorithm for computing geodesics on the universal Teichmüller space T (1) in the Weil-Petersson (WP ) metric. Another realization for T (1) is the space of planar shapes, modulo translation and scale, and thus our algorithm addresses a fundamental problem in computer vision: compute the distance between two given shapes. The identification of smooth shapes with eleme...