Related papers: The Teichm\"uller Stack

We show that the Teichm\"uller space of a surface without boundary and with punctures, equipped with Thurston's metric is the limit (in an appropriate sense) of Teichm\"uller spaces of surfaces with boundary, equipped with their arc…

Given a proper morphism X -> S, we show that a large class of objects in the derived category of X naturally form an Artin stack locally of finite presentation over S. This class includes S-flat coherent sheaves and, more generally,…

We consider the moduli problem of stable maps from a Riemann surface into a supermanifold; in twistor-string theory, this is the instanton moduli space. By developing the algebraic geometry of supermanifolds to include a treatment of…

We consider cyclic $m$-isometries on a complex separable Hilbert space. Such operators are characterized in terms of shifts on abstract spaces of weighted Dirichlet type. Our results resemble those of Agler and Stankus, but our model spaces…

We consider a specific class of infinite dimensional $p$-adic Lie groups, i.e., a sort of diffeomorphism groups on $p$-adic ball $\operatorname{Diff}^{\operatorname{an}}(B_\epsilon)$. It turns out that this group has a natural logarithmic…

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 show that the inertia stack of a topological stack is again a topological stack. We further observe that the inertia stack of an orbispace is again an orbispace. We show how a U(1)-banded gerbe over an orbispace gives rise to a flat line…

The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of…

The Teichm\"uller harmonic map flow is a gradient flow for the harmonic map energy of maps from a closed surface to a general closed Riemannian target manifold of any dimension, where both the map and the domain metric are allowed to…

In this paper, certain natural and elementary polygonal objects in Euclidean space, {\it the stable polygons}, are introduced, and the novel moduli spaces ${\bfmit M}_{{\bf r}, \epsilon}$ of stable polygons are constructed as complex…

Let $G$ be a finitely generated Kleinian group and let $\Delta$ be an invariant collection of components in its region of discontinuity. The Teichm\"uller space $T(\Delta,G)$ supported in $\Delta$, is the space of equivalence classes of…

We consider circle patterns on closed tori equipped with complex projective structures. There is an embedding of the space of circle patterns to the Teichm\"{u}ller space of a punctured surface. Via the embedding, the Weil-Petersson…

In this paper we prove that for all $n=4k-2$, $k\ge2$ there exists a closed smooth complex hyperbolic manifold $M$ with real dimension $n$ having non-trivial $\pi_1(\mathcal{T}^{<0}(M))$. $\mathcal{T}^{<0}(M)$ denotes the Teichm\"uller…

The Teichm\"uller space of a closed set in the Riemann sphere is a simply connected complex Banach manifold. Its complex structure follows from Lieb isomorphism. In this paper, we show the conformal naturality of Lieb isomorphism. We then…

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…

We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length $\leq L$ on an arbitrary closed, orientable, negatively curved surface. More generally, we…

We introduce a class of diffeological spaces, called elastic, on which the left Kan extension of the tangent functor of smooth manifolds defines an abstract tangent functor in the sense of Rosicky. On elastic spaces there is a natural…

The Bers embedding of theTeichm\"uller space is a homeomorphism into the Banach space of certain holomorphic automorphic forms. For a subspace of the universal Teichm\"uller space and its corresponding Banach subspace, we consider whether…

We give a real-analytic section for the Teichm\"uller projection onto the VMO-Teichm\"uller space by using the variant of Beurling-Ahlfors extension by heat kernel introduced by Fefferman, Kenig and Pipher in 1991. Based on this result, we…

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the…