2. The universal Teichm¨ uller space

Taking the “anabelian yoga” (which remains conjectural) into account, which says that an an- abelian algebraic curve over a number field K (finite extension of Q ) is known up

can be used to produce a natural cell decomposition of the Teichm¨ uller space of a compact surface with non-empty boundary and negative Euler characteristic.. We will show that

The Teichm¨ uller space of hyperbolic metrics with geodesic boundary and cusp ends on Σ is denoted by T (Σ).. If the subsurface is compact, then it is incompressible if and only if

We remark that although the iterative algorithm is designed for obtaining an extremal map between connected surfaces with given boundary values, the conver- gence proof applies

A landmark constrained T-Map is the unique mapping between genus-1 surfaces that minimizes the maximal conformality distortion while matching the prescribed feature

Recently, a simple iterative algorithm for computing the Teichm¨ uller maps between connected Riemann surfaces with given boundary value was proposed in [11].. Numerical results

Here we propose a novel and intrinsic method to compute surface Teichm¨ uller space coordinates (shape indices) and we apply it to study brain morphometry in Alzheimers disease (AD)

Considerations include expansions for the WP pairing of gradients, expansions for the Hessian and co- variant derivative, comparability models for the WP metric, as well as the