Related papers: On transverse $R$-covered minimal foliations

This paper, which is an outgrowth of a previous paper of the authors, continues the study of dimension 1 foliations on non-metrisable manifolds emphasising some anomalous behaviours. We exhibit surfaces with various extra properties like…

Given an Anosov flow on a closed 3-manifold, we are interested in the problem of whether or not making non-trivial Fried surgeries along a finite set of periodic orbits can produce a flow equivalent to itself. We show that for some…

We consider Anosov flows on closed 3-manifolds preserving a volume form $\Omega$. Following Dyatlov and Zworski (2017) we study spaces of invariant distributions with values in the bundle of exterior forms whose wavefront set is contained…

We extend an energy introduced by Mather to the setting of Almgren-Pitts min-max theory and obtain a parametric, higher-dimensional analogue of Mather's variational barrier theory for twist maps and geodesics on tori. We use this energy to…

Using the quotient bundle introduced by Wojtkowski, we give necessary and sufficient conditions for a magnetic flow on a closed, oriented surface to be Anosov.

In this paper, we study transversely holomorphic partially hyperbolic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove in the seven-dimensional case that under the assumption that the subcenter…

In this paper, we describe a new approach to the problem of classification of transitive Anosov flows on 3-manifolds up to orbital equivalence. More specifically, generalizing the notion of Markov partition, we introduce the notion of…

Let M be a closed orientable irreducible 3-manifold, and let f be a diffeomorphism over M. We call an embedded 2-torus T an Anosov torus if it is invariant and the induced action of f over \pi_1(T) is hyperbolic. We prove that only few…

For finitely generated groups, amenability and F{\o}lner properties are equivalent. However, contrary to a widespread idea, Kaimanovich showed that F{\o}lner condition does not imply amenability for discrete measured equivalence relations.…

In the hyperspace of subcontinua of a compact surface we consider a second order Hausdorff distance. This metric space is compactified in such a way that the stable foliation of a pseudo-Anosov map is naturally identified with a…

We prove that if F is a foliation of a compact manifold M with all leaves compact submanifolds, and the transverse saturated category of F is finite, then the leaf space M/F is compact Hausdorff. The proof is surprisingly delicate, and is…

We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a…

In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $\xi$ defined on a neighborhood of the closure of a bounded…

For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner's construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points,…

We prove that every transitive topologically Anosov flow on a closed 3-manifold is orbitally equivalent to a smooth Anosov flow, preserving an ergodic smooth volume form.

This paper compares two invariants of foliated manifolds which seem to measure the non-Hausdorffness of the leaf space: the transversal length on the fundamental group and the foliated Gromov norm on the homology. We consider foliations…

We study Anosov families which are sequences of diffeomorphisms along compact Riemannian manifolds such that the tangent bundle split into expanding and contracting subspaces. In this paper we prove that a certain class of Anosov families:…

We prove the existence of a one parameter family of minimal embedded hypersurfaces in $R^{n+1}$, for $n \geq 3$, which generalize the well known 2 dimensional "Riemann minimal surfaces". The hypersurfaces we obtain are complete, embedded,…

Let $d\geq2$ be an integer. The set $\mathbf{F}(d)$ of foliations of degree $d$ on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension $d^2+4d+2$ on which $\mathrm{Aut}(\mathbb…

In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3-dimensional flat torus must be…