Related papers: Non rigidity of hyperbolic laminations

In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those…

We study unknottedness for free boundary minimal surfaces in a three-dimensional Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary, and for self-shrinkers in the three-dimensional Euclidean space. For doing…

We show that for every $\epsilon>0$, there exists a compact lamination by $\epsilon$-holomorphic surfaces in the complex projective plane, minimal, and that carries hyperbolic holonomy. We call $\epsilon$-holomorphic a real 2-dimensional…

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 shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called `flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When equality holds in this inequality, we show that all the ends…

We characterization hyperbolic metrics on compact surfaces with boundary using a variational principle. As a consequence, a new parametrization of the Teichmuller space of compact surface with boundary is produced. In the new…

In the present paper, we revisit a famous theorem by Candel that we generalize by proving that given a compact lamination by hyperbolic surfaces, every negative function smooth inside the leaves and transversally continuous is the curvature…

We prove that there are Fenchel-Nielsen coordinates for the Teichmueller space of a finite area hyperbolic surface with respect to which the length functions are convex.

We prove flatness of complete Riemannian planes and cylinders without conjugate points under optimal conditions on the area growth.

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichm\"uller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

We prove that an infinite Riemann surface $X$ is parabolic ($X\in O_G$) if and only if the union of the horizontal trajectories of any integrable holomorphic quadratic differential that are cross-cuts is of zero measure. Then we establish…

In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $\sigma$ on the smooth locus, and for which every finite…

The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of "warped polyhedra" with a fixed metric on the…

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.

We show that every $\mathbb R$-linear surjective isometry between the cotangent spaces to the Teichm\"uller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces, which is an analogue…

For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles…

Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{D})$ is the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of $\mathbb{D}$. A geodesic ray in $T(\mathbb{D})$ is of Teichm\"uller type if it…

We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $\chi$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This…

We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi--Yau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact…

Log-Riemann surfaces of finite type are Riemann surfaces with finitely generated fundamental group equipped with a local diffeomorphism to C such that the surface has finitely many infinite order ramification points. We define and prove…