Related papers: The Arnoux-Yoccoz Teichmueller disc

Let $X$ be a smooth compact connected manifold. Let $G=\mbox{Diff}\, X$ be the group of diffeomorphisms of $X$, equipped with the $C^\infty$-topology, and let $H$ be the stabilizer of some point in $X$. Then the inclusion $H\to G$, which is…

In this work we completely classify $C^\infty$ conjugacy for conservative partially hyperbolic diffeomorphisms homotopic to a linear Anosov automorphism on the 3-torus by its center foliation behavior. We prove that the uniform version of…

Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length…

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays…

We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse…

In this paper, we focus on the rigidity of $C^{2+}$-smooth codimension-one stable foliations of Anosov diffeomorphisms. Specifically, we show that if the regularity of these foliations is slightly bigger than $2$, then they will have the…

For a nonlinear Anosov diffeomorphism of the 2-torus, we present examples of measures so that the group of $\mu$-preserving diffeomorphisms is, up to zero-entropy transformations, cyclic. For families of equilibrium states $\mu$, we…

We study almost complex surfaces in the nearly K\"ahler $S^3\times S^3$. We show that there is a local correspondence between almost complex surfaces and solutions of the H-surface equation introduced by Wente. We find a global holomorphic…

We study a class of exceptional minimal surfaces in spheres for which all Hopf differentials are holomorphic. Extending results of Eschenburg and Tribuzy \cite{ET0}, we obtain a description of exceptional surfaces in terms of a set of…

This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichm\"uller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for…

In this note we describe a family of arguments that link the homotopy-type of a) the diffeomorphism group of the disc $D^n$, b) the space of co-dimension one embedded spheres in a sphere and c) the homotopy-type of the space of co-dimension…

We classify the non arithmetic rank one affine invariant orbifolds that do not arise from Veech surfaces in H(3,1) and H^odd(2,2). We also give rigidity results on the isoperiodic leaf of non arithmetic Veech surfaces.

For Hoelder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hoelder-continuous on compact sets of measure arbitrarily close to 1. The results extend to…

A finite subset S of a closed hyperbolic surface F canonically determines a "centered dual decomposition" of F: a cell structure with vertex set S, geodesic edges, and 2-cells that are unions of the corresponding Delaunay polygons. Unlike a…

Let $f$ be a non-invertible partially hyperbolic endomorphism on $\mathbb{T}^2$ which is derived from a non-expanding Anosov endomorphism. Differing from the case of diffeomorphisms derived from Anosov automorphisms, there is no a priori…

For a given smooth $2$-knot in $S^4$, we relate the existence of a smooth Seifert hypersurface of a certain class to the existence of irreducible $ SU(2)$-representations of its knot group. For example, we see that any smooth $2$-knot…

A closed symmetric differential of the 1st kind is a differential that locally is the product of closed holomorphic 1-forms. We show that closed symmetric 2-differentials of the 1st kind on a projective manifold $X$ come from maps of $X$ to…

We prove that there exists an open subset of the set of real-analytic Hamiltonian diffeomorphisms of a closed surface in which diffeomorphisms exhibiting fast growth of the number of periodic points are dense. We also prove that there…

Expanding on work by Conway, Orson, and Powell, we study the isotopy classes rel. boundary of nonorientable, compact, locally flatly embedded surfaces in $D^4$ with knot group $\mathbb{Z}_2$. In particular we show that if two such surfaces…

We provide minimal constructions of meanders with particular combinatorics. Using these meanders, we give minimal constructions of hyperelliptic pillowcase covers with a single horizontal cylinder and simultaneously a single vertical…