Polynomial invariants for fibered 3-manifolds and teichmüller geodesics for foliations
Quasiconformal mappings of Y-pieces.
In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.
Quasihomographies in the theory of Teichmüller spaces [Book]
Quasi-projections in Teichmüller space.
Rectifiability in Teichmüller theory
Reduced Bers boundaries of Teichmüller spaces
We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space lying there into a point.This boundary turns out to be independent of the basepoint, and the action of the mapping class group extends continuously to this boundary.This is an affirmative answer to Thurston’s conjecture.He also conjectured that this boundary is homeomorphic to the unmeasured lamination space by the correspondence coming...
Riemann surfaces with boundary and natural triangulations of the Teichmüller space
We compare some natural triangulations of the Teichmüller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell–Wolf’s proof to show that grafting semi-infinite cylinders at the ends of hyperbolic surfaces with fixed boundary lengths is a homeomorphism. This way, we construct a family of equivariant triangulations of the Teichmüller space of punctured surfaces that interpolates between Bowditch–Epstein–Penner’s (using the spine construction) and Harer–Mumford–Thurston’s...
Riemann Surfaces with Shortest Geodesic of Maximal Length.
Riemannian metrics on Teichmüller space.
Sharp norm estimate of Schwarzian derivative for a class of convex functions
We establish a sharp norm estimate of the Schwarzian derivative for a function in the classes of convex functions introduced by Ma and Minda [Proceedings of the Conference on Complex Analysis, Int. Press, 1992, 157-169]. As applications, we give sharp norm estimates for strongly convex functions of order α, 0 < α < 1, and for uniformly convex functions.
Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
Stability of the homology of the moduli spaces of Riemann surfaces with spin structure.
Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely,...
Strengthening pseudoconvexity of finite-dimensional Teichmüller spaces.
Substantial boundary points for plane domains and Gardiner's conjecture.
Teichmüller space is not Gromov hyperbolic.
Teichmüller spaces and BMOA.
Teichmüller spaces are not starlike.
Teichmüller spaces with variable bases in the universal Teichmüller space.
Teichmüller theory of bordered surfaces.