Related papers: The horofunction compactification of Teichm\"uller…

Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular…

In a recent paper \cite{T} the fact that a class of locally compact metric spaces $X$, among which are Euclidean spaces, are not homemorphic to their punctured version $X\men\{p\}$, was given an interesting new proof which does not use…

It is known that some GIT compactifications associated to moduli spaces of either points in the projective line or cubic surfaces are isomorphic to Baily-Borel compactifications of appropriate ball quotients. In this paper, we show that…

In this paper, we construct a compactification of the space of Bridgeland stability conditions on a smooth projective curve, as an analogue of Thurston compactifications in Teichm\"uller theory. In the case of elliptic curves, we compare…

The aim of this paper is to study further the universal toric genus of compact homogeneous spaces and their homogeneous fibrations. We consider the homogeneous spaces with positive Euler characteristic. It is well known that such spaces…

The Urysohn universal metric space U is characterized up to isometry by the following properties: (1) U is complete and separable; (2) U contains an isometric copy of every separable metric space; (3) every isometry between two finite…

The problem of holomorphic contractibilty of Teichm\"uller spaces T(0, n) of the punctures spheres (n > 4) arose in the 1970s in connection with solving the algebraic equations in Banach algebras. We provide a positive solution of this…

We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model $\mathcal {V}(S)$ which is induced by the cone metric over the complex of curves. As an application, we know…

In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichm{\"u}ller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit sphere at each point in the tangent space…

We construct a new Riemannian metric on Goldman space $\mathcal{B}(S)$, the space of the equivalence classes of convex projective structures on the surface $S$, and then prove the new metric, as well as the metric of Darvishzadeh and…

If $p : Y \to X$ is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to $p$, from the Teichm\"uller space ${\cal T}(X)$, for $X$, to ${\cal…

We determine the homeomorphism type of the space of smooth complete nonnegatively curved metrics on surfaces of positive Euler characteristic equipped with the topology of $C^\gamma$ uniform convergence on compact sets, when $\gamma$ is…

Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…

This is the second paper in a series of investigations of the pluripotential theory on Teichm\"uller space. The main purpose of this paper is to establish the Poisson integral formula for pluriharmonic functions on Teichm\"uller space which…

We construct an Ahlfors-Bers complex analytic model for the Teichm\"uller space of the universal hyperbolic lamination (also known as Sullivan's Teichm\"uller space) and the renormalized Weil-Petersson metric on it as an extension of the…

This paper constructs a Hodge theory of noncompact topologically tame manifolds $M$. The main result is an isomorphism between the de Rham cohomology with compact supports of $M$ and the kernel of the Hodge--Witten--Bismut Laplacian…

It was recently shown that the Carath\'eodory and Teichm\"uller metrics on the Teichm\"uller space of a closed surface do not coincide. On the other hand, Kra earlier showed that the metrics coincide when restricted to a Teichm\"uller disk…

In this paper, we aim to establish a new shape theory, compact Hausdorff shape (CH-shape) for general Hausdorff spaces. We use the "internal" method and direct system approach on the homotopy category of compact Hausdorff spaces. Such a…

In this paper we construct a compactification for the parameter space of convex projective structures on a fixed n-manifold M. This parameter space is a closed semi-algebraic subset of the variety of characters of representations of the…

We study the Carath\'eodory metric on some generalized Teichm\"uller spaces. Earle showed that the Carath\'eodory metric is complete on any Teichm\"uller space. Miyachi extended this result for Asymptotic Teichm\"uller spaces. We study the…