Related papers: Isometric disks are holomorphic

We show that the length spectrum metric on Teichm\"uller spaces of surfaces of infinite topological type is complete. We also give related results and examples that compare the length spectrum Teichm\"uller space with quasiconformal and the…

The $L^1$-$L^\infty$ geometry is the Finsler geometry of the Teichm\"uller space by the Teichm\"uller metric and the $L^1$-norm function of holomorphic quadratic differentials. In this paper, aiming to develop the $L^1$-$L^\infty$-geometry…

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…

The paper is devoted to a description of all strongly facially symmetric spaces which are isometrically isomorphic to $L_1$-spaces. We prove that if $Z$ is a real neutral strongly facially symmetric space such that every maximal geometric…

We show that if a compact Kahler manifold X admits a cohomologically hyperbolic surjective endomorphism then its Kodaira dimension is non-positive. This gives an affirmative answer to a conjecture of Guedj in the holomorphic case. The main…

We show in this paper that every domain in a separable Hilbert space, say $\cH$, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of $\cH$. This is…

We extend the concept of a finite dimensional {\it holomorphic homogeneous regular} (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of…

Let $\Sigma$ be a Riemann surface of genus $g$ bordered by $n$ curves homeomorphic to the circle $\mathbb{S}^1$, and assume that $2g+2-n>0$. For such bordered Riemann surfaces, the authors have previously defined a Teichm\"uller space which…

A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly).…

A hyperbolic 0-metric on a surface with boundary is a hyperbolic metric on its interior, exhibiting the boundary behavior of the standard metric on the Poincar\'e disk. Consider the infinite-dimensional Teichm\"uller spaces of hyperbolic…

In this paper we focus on the integrable Teichm\"uller spaces, subspaces of the universal Teichm\"uller space, and we prove that elements of some of them are continuously differentiable.

We prove some sharp inequalities for complex harmonic functions on the unit disk. The results extend a M. Riesz conjugate function theorem and some well-known estimates for holomorphic functions. We apply some of results to the…

We study the K\"ahler-Einstein manifolds which admits a holomorphic isometry into either the generalized Burns-Simanca manifold $(\tilde {\mathbb C}^n, g_S)$ or the Eguchi-Hanson manifold $(\tilde {\mathbb C}^2, g_{EH})$. Moreover, we prove…

Let $\,G/K\,$ be a non-compact irreducible Hermitian symmetric space of rank $\,r\,$ and let $\,NAK\,$ be an Iwasawa decomposition of $\,G$. By the polydisc theorem, $\,AK/K\,$ can be regarded as the base of an $\,r$-dimensional tube domain…

We study proper holomorphic maps between bounded symmetric domains $D$ and $\Omega$. In particular, when $D$ and $\Omega$ are of the same rank $\ge 2$ such that all irreducible factors of $D$ are of rank $\ge 2$, we prove that any proper…

Consider a holomorphic map $F: D \to G$ between two domains in ${\mathbb C}^N$. Let $\mathcal F$ denote a family of geodesics for the Kobayashi distance, such that $F$ acts as an isometry on each element of $\mathcal F$. This paper is…

It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic. In other words, each two points of this space (each…

Let X_0 be a compact connected Riemann surface of genus g with D_0\subset X_0 an ordered subset of cardinality n, and let E_G be a holomorphic principal G-bundle on X_0, where G is a complex reductive affine algebraic group, that admits a…

Supersymmetric domain-wall spacetimes that lift to Ricci-flat solutions of M-theory admit generalized Heisenberg (2-step nilpotent) isometry groups. These metrics may be obtained from known cohomogeneity one metrics of special holonomy by…

We prove that geodesic balls centered at some base point are isoperimetric in the real hyperbolic space $H_{\mathbb R}^n$ endowed with a smooth, radial, strictly log-convex density on the volume and perimeter. This is an analogue of the…