Related papers: Higher Bers maps

We investigate expansive Hilbert space operators $T$ that are finite rank perturbations of isometric operators. If the spectrum of $T$ is contained in the closed unit disc $\overline{\mathbb{D}}$, then such operators are of the form $T=…

Let $S$ be a closed Riemann surface of genus $g(\geqq 2)$ and set $\dot{S}=S \setminus \{\hat{z}_0 \}$. Then we have the composed map $\varphi\circ r$ of a map $r: T(S) \times U \rightarrow F(S)$ and the Bers isomorphism $\varphi: F(S)…

Using the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces and some of their other complex geometric features, we prove a general theorem on maximization of homogeneous polynomial (in fact, more general…

Lipman Bers' universal Teichm\"uller space, classically denoted by $T(1)$, plays a significant role in Teichm\"uller theory, because all the Teichm\"uller spaces $T(G)$ of Fuchsian groups $G$ can be embedded into it as complex submanifolds.…

In this paper we parametrize the Teichm\"uller spaces of constructible Koebe groups, that is Kleinian group that arise as covering of $2-$orbifolds determined by certain normal subgroups of their fundamental groups. We also study the…

We study classes of locally biholomorphic mappings defined in the $\P$ that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations…

We prove that the fiber space consisting of BMOA functions that are the logarithms of derivatives of conformal homeomorphisms of the unit disk onto bounded quasidisks forms a real-analytic disk bundle over the Bers embedding of the BMO…

We develop a real-analytic counterpart of the Bers embedding for the Fr\'echet Lie group $\Diff^{-\infty}(\R)$ of decay-controlled diffeomorphisms of the line, and establish its connection to $L^p$ Fisher-Rao geometry on densities. For…

We start by describing how ideal triangulations on a surface degenerate under pinching of a multicurve. We use this process to construct a homomorphism from the Ptolemy groupoid of a surface to that of a pinched surface which is natural…

Let $(M,F)$ be a Finsler manifold. We construct a 1-cocycle on $\Diff(M)$ with values in the space of differential operators acting on sections of some bundles, by means of the Finsler function $F.$ As an operator, it has several…

In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…

In the first part of the paper we describe the complex geometry of the universal Teichm\"uller space $\mathcal T$, which may be realized as an open subset in the complex Banach space of holomorphic quadratic differentials in the unit disc.…

We develop the Titchmarsh-Weyl theory for vector-valued discrete Schr\"odinger operators and show that the Weyl $m$ functions associated with these operators map complex upper half plane to the Siegel upper half space. We also discuss about…

In this paper we introduce new spaces of holomorphic functions on the pointed unit disc of $\mathbb C$ that generalize classical Bergman spaces. We prove some fundamental properties of these spaces and their dual spaces. We finish the paper…

It is known that every finitely unbranched covering $\alpha:\widetilde{S}_{g(\alpha)}\rightarrow S$ of a compact Riemann surface $S$ with genus $g\geq2$ induces an isometric embedding $\Gamma_{\alpha}$ from the Teichm\"uller space $T(S)$ to…

Recently the author has presented a new approach to solving extremal problems of geometric function theory. It involves the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces. We show here that this approach,…

In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a…

We consider the mapping $b_L\colon\mathcal{T} \to \chi$ from the Fricke-Teichm\"uller space $\mathcal{T}$ into the $\mathrm{PSL}_2\mathbb{C}$-character variety $\chi$ of the surface, obtained by bending Fuchsian representations along a…

We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disc removed. We define a refined Teichmueller space of such Riemann surfaces and demonstrate that in…

In this paper, we introduce a new variation of the Teichm\"{u}ller space, namely the deformation space of hyperbolic structures on a surface with both enhancement and decoration. We construct the parameterization of this deformation space,…