Related papers: Hyperbolic spaces in Teichm\"uller spaces

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

In this paper, we parametrize the space of isometric immersions of the hyperbolic plane into the hyperbolic 3-space in terms of null-causal curves in the space of oriented geodesics. Moreover, we characterize "ideal cones" (i.e., cones…

In this paper, we show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic $3$-manifolds except some special cases.

A Teichm\"uller space $Teich$ is a quotient of the space of all complex structures on a given manifold $M$ by the connected components of the group of diffeomorphisms. The mapping class group $\Gamma$ of $M$ is the group of connected…

Let $\Sigma$ be a connected, oriented surface with punctures and negative Euler characteristic. We introduce wild globally hyperbolic anti-de Sitter structures on $\Sigma \times \mathbb{R}$ and provide two parameterisations of their…

We equip the whole tangent space $TM$ to a hyperbolic manifold $M$ (of constant sectional curvature -1) with a natural metric in an intrinsic way, so that the isometries of $M$ extend to isometries of $TM$ by holomorphic continuation. The…

We verify that the $p$-integrable Teichm\"uller space $T_p$ admits the canonical complex Banach manifold structure for any $p \geq 1$. Moreover, we characterize a quasisymmetric homeomorphism corresponding to an element of $T_p$ in terms of…

We show that the moduli space M of marked cubic surfaces is biholomorphic to the quotient by a discrete group generated by complex reflections of the complex four-ball minus the reflection hyperplanes of the group. Thus M carries a complex…

Kahn and Markovic \cite{KahnMark} proved that the fundamental group of each closed hyperbolic three manifold contains a closed surface subgroup. One of the main ingredients in their proof is a theorem which states that an assignment of…

Let X be a smooth complex projective curve and S a finite subset of X. We show that an orthogonal or symplectic parabolic Higgs bundle on X with parabolic structure over S admits a Hermitian-Einstein connection if and only if it is…

Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood…

In our previous paper with the same title, we established the complex Banach manifold structure for the Teichm\"uller space of circle diffeomorphisms whose derivatives belong to the Zygmund class. This was achieved by demonstrating that the…

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

We show that in an L-annularly linearly connected, N-doubling, complete metric space, any n points lie on a K-quasi-circle, where K depends only on L, N and n. This implies, for example, that if G is a hyperbolic group that does not split…

We describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using our methods we then prove that a finitely generated group $H$ admitting a quasi-isometric map $\phi$ into a…

We study the geometry of the Thurston metric on the Teichm\"uller space $\mathcal{T}(S)$ of hyperbolic structures on a surface $S$. Some of our results on the coarse geometry of this metric apply to arbitrary surfaces $S$ of finite type;…

In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…

We first describe the action of the fundamental group of a closed surface of variable negative curvature on the oriented geodesics in its universal covering in terms of a naturally-defined flat connection whose holonomy lies in the group of…

In our previous paper, we discussed the hyperbolization of the configuration space of n(> 4) marked points with weights in the projective line up to projective transformations. A variation of the weights induces a deformation. It was shown…

A Hamiltonian embedding is an embedding of a graph $G$ such that the boundary of each face is a Hamiltonian cycle of $G$. It is shown that the hypercube graph $Q_n$ admits such an embedding on an orientable surface when $n$ is a power of 2.…