相关论文: Teichm\"uller spaces and bounded symmetric domains…

We study isometric maps between Teichm\"uller spaces and bounded symmetric domains in their intrinsic Kobayashi metric. From a complex analytic perspective, these two important classes of geometric spaces have several features in common but…

This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichm\"uller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichm\"uller disk.…

In this paper we introduce a new class of domains -- log-type convex domains, which have no boundary regularity assumptions. Then we will localize the Kobayashi metric in log-type convex subdomains. As an application, we prove a local…

Caratheodory's and Kobayashi's metrics on Teichmueller spaces of dimension two or more are never equal in the direction of any tangent vector defined by a separating cylindrical differential

This article considers isometries of the Kobayashi and Carath\'{e}od-ory metrics on domains in $ \mathbf{C}^n $ and the extent to which they behave like holomorphic mappings. First we prove a metric version of Poincar\'{e}'s theorem about…

In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First we show that for a $C^1$-smooth totally geodesic Kobayashi isometric embedding $f\colon \Omega\to\Omega'$…

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

In this paper, we shall show that the metric boundary of the Teichmueller space with respect to the Teichmueller distance contains non-Busemann points when the complex dimension of the Teichmueller space is at least two.

We describe in elementary geometrical terms Teichm\" uller spaces of decorated and holed surfaces. We construct explicit global coordinates on them as well as on the spaces of measured laminations with compact and closed support…

We show that the horofunction boundary of Teichm\"uller space with Thurston's Lipschitz metric is the same as the Thurston boundary. We use this to determine the isometry group of the Lipschitz metric, apart from in some exceptional cases.…

We outline old and new results concerning the well-known problems in the Teichm\"uller space theory, i.e., whether these spaces are starlike in the Bers holomorphic embedding and whether any Teichm\"uller space of dimension greater than 1…

Given a compact K\"ahler manifold, we prove that all global isometries of the space of K\"ahler metrics are induced by biholomorphisms and anti-biholomorphisms of the manifold. In particular, there exist no global symmetries for Mabuchi's…

We prove that the Teichm\"{u}ller space $\mathscr{T}$ of a closed surface of genus $g \ge 2$ cannot be biholomorphic to any domain which is locally strictly convex at some boundary point.

We prove that the every quasi-isometry of Teichm\"uller space equipped with the Teichm\"uller metric is a bounded distance from an isometry of Teichm\"uller space. That is, Teichm\"uller space is quasi-isometrically rigid.

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…

In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.

We study two $2$-dimensional Teichm\"uller spaces of surfaces with boundary and marked points, namely, the pentagon and the punctured triangle. We show that their geometry is quite different from Teichm\"uller spaces of closed surfaces.…

Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichm\"uller spaces. We show that for dimension at least $2$, all isometric embeddings arise from branched coverings. This generalizes a…

We study the class of holomorphic and isometric submersions between finite-type Teichm\"uller spaces. We prove that, with potential exceptions coming from low-genus phenomena, any such map is a forgetful map $\mathcal{T}_{g,n} \rightarrow…