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Bers slices are Zariski dense  [PDF]
David Dumas,Richard P. Kent IV
Mathematics , 2008, DOI: 10.1112/jtopol/jtp014
Abstract: We prove that every Bers slice of quasi-Fuchsian space is Zariski dense in the character variety.
Higher Bers maps  [PDF]
Guy Buss
Mathematics , 2008,
Abstract: The Bers embebbing realizes the Teichm\"uller space of a Fuchsian group $G$ as a open, bounded and contractible subset of the complex Banach space of bounded quadratic differentials for $G$. It utilizes the schlicht model of Teichm\"uller space, where each point is represented by an injective holomorphic function on the disc, and the map is constructed via the Schwarzian differential operator. In this paper we prove that a certain class of differential operators acting on functions of the disc induce holomorphic mappings of Teichm\"uller spaces, and we also obtain a general formula for the differential of the induced mappings at the origin. The main focus of this work, however, is on two particular series of such mappings, dubbed higher Bers maps, because they are induced by so-called higher Schwarzians -- generalizations of the classical Schwarzian operator. For these maps, we prove several further results. The last section contains a discussion of possible applications, open questions and speculations.
Projective structures with degenerate holonomy and the Bers density conjecture  [PDF]
Kenneth Bromberg
Mathematics , 2002,
Abstract: We prove the Bers' density conjecture for singly degenerate Kleinian surfaces groups without parabolics.
Reduced Bers boundaries of Teichmüller spaces  [PDF]
Ken'ichi Ohshika
Mathematics , 2011,
Abstract: We consider a quotient space of the Bers boundary of Teichm\"{u}ller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space into a point. This reduced Bers boundary turns out to be independent of the basepoint, and the action of the mapping class group on the Teichm\"{u}ller space extends continuously to this boundary. We show that every auto-homeomorphism on the reduced Bers boundary comes from an extended mapping class. We also give a way to determine the limit in the reduced Bers boundary up to some ambiguity for parabolic curves for a given sequence in the Teichm\"{u}ller space, by generalising the Thurston compactification.
Bers' constants for punctured spheres and hyperelliptic surfaces  [PDF]
Florent Balacheff,Hugo Parlier
Mathematics , 2009,
Abstract: This article is dedicated to prove Buser's conjecture about Bers' constants for spheres with cusps (or marked points) and for hyperelliptic surfaces. More specifically, our main theorem states that any hyperbolic sphere with $n$ cusps has a pants decomposition with all of its geodesics of length bounded by a constant roughly square root of $n$. Other results include lower and upper bounds for Bers' constants for hyperelliptic surfaces and spheres with boundary geodesics.
Bers isomorphism on the universal Teichmüller curve  [PDF]
Lee-Peng Teo
Mathematics , 2006,
Abstract: We study the Bers isomorphism between the Teichm\"uller space of the parabolic cyclic group and the universal Teichm\"uller curve. We prove that this is a group isomorphism and its derivative map gives a remarkable relation between Fourier coefficients of cusp forms and Fourier coefficients of vector fields on the unit circle. We generalize the Takhtajan-Zograf metric to the Teichm\"uller space of the parabolic cyclic group, and prove that up to a constant, it coincides with the pull back of the Velling-Kirillov metric defined on the universal Teichm\"uller curve via the Bers isomorphism.
On extendibility of a map induced by Bers isomorphism  [PDF]
Hideki miyachi,Toshihiro Nogi
Mathematics , 2014,
Abstract: 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 $\varphi: F(S) \rightarrow T(\dot{S})$, where $F(S)$ is the Bers fiber space of $S$, $T(X)$ is the Teichm\"uller space of $X$ and $U$ is the upper half-plane. The purpose of this paper is to show the map $\varphi\circ r:T(S)\times U \rightarrow T(\dot{S})$. has a continuous extension to some subset of the boundary $T(S) \times \partial U$.
On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains  [PDF]
Steven G. Krantz
Mathematics , 2013,
Abstract: We study and generalize a classical theorem of L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group.
Weighted Composition Operators between Bers-type Spaces

Wang Maofa,Liu Yun,

数学物理学报(A辑) , 2007,
Abstract: In this paper,the authors study weighted composition operators between Bers-type spaces.Some sufficient and necessary conditions for such operators to be bounded,compact and weakly compact are given,respectively.This may be regarded as a generalization of the corresponding multiplication operator and composition operator cases.As a corollary, the authors obtain that the weak compactness and the compactness of weighted composition operators between Bers-type spaces are equivalent.In addition,the authors also characterize composition operators which have Fredholm properties and closed range on Bers-type spaces, respectively.
The Bers-Greenberg Theorem and the Maskit Embedding for Teichmüller spaces  [PDF]
Pablo Ares-Gastesi
Mathematics , 1995,
Abstract: The Bers-Greenberg theorem tells that the Teichm\"{u}ller space of a Riemann surface with branch points (orbifold) depends only on the genus and the number of special points, but not on the particular ramification values. On the other hand, the Maskit embedding provides a mapping from the Teichm\"{u}ller space of an orbifold, into the product of one dimensional Teichm\"{u}ller spaces. In this paper we prove that there is a set of isomorphisms between one dimensional Teichm\"{u}ller spaces that, when restricted to the image of the Teichm\"{u}ller space of an orbifold under the Maskit embedding, provides the Bers-Greenberg isomorphism.
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