Related papers: Dehn-Fried surgeries on non-transitive expansive f…

We study the transverse geometric behavior of 2-dimensional foliations in 3-manifolds. We show that an R-covered transversely orientable foliation with Gromov hyperbolic leaves in a closed 3-manifold admits a regulating, transverse…

A pseudo-Anosov homeomorphism of a surface is a canonical representative of its mapping class. In this paper, we explain that a transitive pseudo-Anosov flow is similarly a canonical representative of its stable Hamiltonian class. It…

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…

Using bi-contact geometry, we define a new type of Dehn surgery on an Anosov flow with orientable weak invariant foliations. The Anosovity of the new flow is strictly connected to contact geometry and the Reeb dynamics of the defining…

Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend…

For certain pseudo-Anosov flows $\phi$ on closed $3$-manifolds, unpublished work of Agol--Gu\'eritaud produces a veering triangulation $\tau$ on the manifold $M$ obtained by deleting $\phi$'s singular orbits. We show that $\tau$ can be…

We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed $3$-manifold (and more general Anosov-like actions) can be seen as an isometric action on a Gromov-hyperbolic space. When the flow is not $\R$-covered,…

In this paper we analyze the long-time behaviour of 3 dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric…

Every pseudo-Anosov flow $\phi$ in a closed $3$-manifold $M$ gives rise to an action of $\pi_1(M)$ on a circle $S^{1}_{\infty}(\phi)$ from infinity \cite{Fen12}, with a pair of invariant \emph{almost} laminations. From certain actions on…

We construct non-algebraic Anosov flows in dimension $3+2n$, $n\geq 2$, by suspending the action of the fundamental group of a finite cover of the Bonatti-Langevin flow.

We provide an exposition of a `horizontal' generalization of Goodman's surgery operation on (pseudo-)Anosov flows. This operation is performed by cutting along a specific kind of annulus that is transverse to the flow and regluing with a…

In this paper, we obtain the existence criteria for a geometic flow on noncompact affine Riemannian manifolds. Our results can be regarded as a real version of Lee-Tam [19]. As an application, we prove that a complete noncompact Hessian…

In this work, we obtain a short time solution for a geometric flow on noncompact affine Riemannian manifolds. Using this result, we can construct a Hessian metric with nonnegative bounded Hessian sectional curvature on some Hessian…

We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of $T^2 \times…

In this paper, we prove that finite-dimensional topological flows without fixed points and having a countable number of periodic orbits, have the small flow boundary property. This enables us to answer positively a question of Bowen and…

We present a new curvature condition which is preserved by the Ricci flow in higher dimensions. For initial metrics satisfying this condition, we establish a higher dimensional version of Hamilton's neck-like curvature pinching estimate.…

In this article we establish the validity of Prandtl layer expansions around Euler flows which are not shear. The presence of non-shear flows at the leading order creates a singularity of $o(\frac{1}{\sqrt{\epsilon}})$. A new $y$-weighted…

Let $M$ be a connected, closed, orientable, irreducible $3$-manifold. We show that: if $M$ admits a co-orientable taut foliation $\mathcal{F}$ with orderable cataclysm, then $\pi_1(M)$ is left orderable. This provides an elementary proof…

We prove that there exists an open and dense subset of the incompressible 3-flows of class C^2 such that, if a flow in this set has a positive volume regular invariant subset with dominated splitting for the linear Poincar\'e flow, then it…

In this paper, we prove that given two $C^1$ foliations $\mathcal{F}$ and $\mathcal{G}$ on $\mathbb{T}^2$ which are transverse, there exists a non-null homotopic loop $\{\Phi_t\}_{t\in[0,1]}$ in $\diff^{1}(\T^2)$ such that…