Related papers: Dominated splitting for exterior powers and singul…

New examples of harmonic unit vector fields on hyperbolic 3-space are constructed by exploiting the reduction of symmetry arising from the foliation by horospheres. This is compared and contrasted with the analogous construction in…

Bounded-type 3-manifolds arise as combinatorially bounded gluings of irreducible 3-manifolds chosen from a finite list. We prove effective hyperbolization and effective rigidity for a broad class of 3-manifolds of bounded type and large…

We introduce a new version of expansiveness similar to separating property for flows. Let $M$ be a compact Riemannian manifold without boundary and $X$ be a $C^1$ vector field on $M$ that generates a flow $\varphi_t$ on $M$. We call $X$…

We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize…

We study coarse separation in one-ended hyperbolic groups from a quantitative point of view, focusing on the volume growth of separating subsets. We prove that a one-ended hyperbolic group that is not virtually a surface group is coarsely…

We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through…

We derive some new conditions for integrability of dynamically defined C^1 invariant splittings in arbitrary dimension and co-dimension. In particular we prove that every 2-dimensional C^1 invariant decomposition on a 3-dimensional manifold…

In this work, we deal with a notion of partially hyperbolic endomorphism. We explore topological properties of this definition and we obtain, among other results, obstructions to get center leaf conjugacy with the linear part, for a class…

In this work we study the existence of singular flows satisfying shadowing-like properties. More precisely, we prove that if C1 -vector field on a closed manifold induces a chain-recurrent flow containing an attached hyperbolic singularity…

Consider a holomorphic foliation with singularities of a 2-dimensional complex manifold. In this article we prove a new sufficient condition for this foliation to have countably many homologically independent complex limit cycles. In…

We establish a correspondence on a Riemann surface between hyperbolic metrics with isolated singularities and bounded projective functions whose Schwarzian derivatives have at most double poles and whose monodromies lie in ${\rm…

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain…

In a variety of settings we provide a method for decomposing a 3-manifold $M$ into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold $M$ is hyperbolic and its volume is bounded below by the sum of the…

We show that a $\mathrm{GL}(d,\mathbb{R})$ cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov…

We introduce two notions of hyperbolicity for not necessarily K\"ahler $n$-dimensional compact complex manifolds $X$. The first, called {\it balanced hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of Gauduchon's…

For a hyperbolic fibered 3-manifold M, we prove results that uniformly relate the structure of surface projections as one varies the fibrations of M. This extends our previous work from the fully-punctured to the general case.

The coexistence of singularities and regular orbits in chain transitive sets has been a major obstacle in understanding the hyperbolic/partial hyperbolic nature of robust dynamics. Notably, the vector fields with all periodic orbits…

We show that the connection between partial breaking of supersymmetry and nonlinear actions is not accidental and has to do with constraints that lead directly to nonlinear actions of the Born-Infeld type. We develop a constrained…

Over the last 10 years or so, advanced statistical properties, including exponential decay of correlations, have been established for certain classes of singular hyperbolic flows in three dimensions. The results apply in particular to the…

Let $\xi$ be an analytic vector field in $\mathbb{R}^3$ with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities $\pi:M\to\mathbb{R}^3$. The union of the images by $\pi$ of the…