Morrey type Teichmüller space and higher Bers maps

Drawing Bers Embeddings of the Teichmüller Space of Once-Punctured Tori

We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmüller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. To each point in the coordinate plane, we first compute the corresponding monodromy representation by numeri...

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

Weighted Composition Operator from Bers-Type Space to Bloch-Type Space on the Unit Ball

In this paper, we characterize the boundedness and compactness of weighted composition operator from Bers-type space to Bloch-type space on the unit ball of Cn. 2010 Mathematics Subject Classification: Primary: 47B38; Secondary: 32A37, 32A38, 32H02, 47B33