Related papers: Normal Smoothings for Charney-Davis Strict Hyperbo…
We prove that smooth cube manifolds have normal smooth structures.
We smooth the singularities of a strictly hyperbolized smooth cube manifold.
We show that the Charney--Davis strict hyperbolization procedure can preserve stable tangent bundles, answering a question of Charney and Davis. The key input is the construction of many hyperbolizing pieces, obtained using separability…
We discuss whether the strict hyperbolization process of Charney and Davis can be done smoothly.
We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence linear and residually finite. Our strategy consists in constructing an action of a…
We prove that non-compact finite volume hyperbolic 3-manifolds that satisfy a mild cohomological condition (infinitesimal rigidity) admit a family of properly convex deformations of their complete hyperbolic structure where the ends become…
In any dimension at least five we construct examples of closed smooth manifolds with the following properties: 1) they have neither real projective nor flat conformal structures; 2) their fundamental group is a non-elementary Gromov…
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting…
We prove that every closed oriented 3-manifold admits a hyperbolic cone-manifold structure with cone-angle arbitrarily close to 2pi.
We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex…
We prove that if two cusped hyperbolic $3$-manifolds admit a regular isomorphism between the profinite completions of their fundamental groups, then they share the same $A$-polynomial and their strongly detected boundary slopes match up.
In this paper, we show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic $3$-manifolds except some special cases.
We define cusp-decomposable manifolds and prove smooth rigidity within this class of manifolds. These manifolds generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume,…
We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0) cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and…
We give a $\delta$-constant criterion for equinormalizability of deformations of isolated (not necessarily reduced) curve singularities over smooth base spaces of dimension $\geq 1$. For one-parametric families of isolated curve…
We prove that completely integrable systems are normalisable in the C infinity category near focus-focus singularities.
We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
We prove that quasi-projective base spaces of smooth families of minimal varieties of general type with maximal variation do not admit Zariski dense entire curves. We deduce the fact that moduli stacks of polarized varieties of this sort…
We prove that stable ergodicity is C r open and dense among conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2,infty]. The proof follows Pugh-Shub program: among conservative partially…