Related papers: Causal Holography of Traversing Flows

We consider Moebius and conformal homeomorphisms $f : \partial X \to \partial Y$ between boundaries of CAT(-1) spaces $X,Y$ equipped with visual metrics. A conformal map $f$ induces a topological conjugacy of the geodesic flows of $X$ and…

We study an incompressible viscous flow around an obstacle with an oscillating boundary that moves by a translational periodic motion, and we show existence of strong time-periodic solutions for small data in different configurations: If…

We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…

In this article, we introduce a new approach to show the existence and smoothing of simple normal crossing varieties in a given projective space. Our approach relates the above to the existence of nowhere reduced schemes called ribbons and…

There is an extensive and growing body of work analyzing convex ancient solutions to Mean Curvature Flow (MCF), or equivalently of Rescaled Mean Curvature Flow (RMCF). The goal of this paper is to complement the existing literature, which…

Let $v$ be a continuous flow with arbitrary singularities on a compact surface. Then we show that if $v$ is non-wandering then $v$ is topologically equivalent to a $C^{\infty}$ flow such that there are no exceptional orbits and $\mathrm{P}…

It is well known that smooth (or continuous) vector fields cannot be topologically transitive on the sphere $\S^2$. Piecewise-smooth vector fields, on the other hand, may present non-trivial recurrence even on $\S^2$. Accordingly, in this…

We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…

In this article, we develop a geometric framework to study the notion of semi-minimality for the generic type of a smooth autonomous differential equation $(X,v)$, based on the study of rational factors of $(X,v)$ and of algebraic…

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily…

We prove that the action of the semigroup generated by a $C^r$ generic pair of area-preserving diffeomorphisms of a compact orientable surface is transitive.

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails…

We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general…

Let $F$ be a transversely oriented foliation of codimension 1 on a closed manifold $M$, and let $\phi=\{\phi^t\}$ be a foliated flow on $(M,F)$. Assume the closed orbits of $\phi$ are simple and its preserved leaves are transversely simple.…

A homeomorphism f of a manifold M is called H_1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover \tM. Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements…

Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real six-dimensional manifolds, can admit G-structures rendering them suitable for internal manifolds in supersymmetric flux compactifications. We develop techniques…

Let $\varphi$ be a transitive pseudo-Anosov flow on an oriented, compact $3$-manifold $M$, possibly with toral boundary. We characterize the surfaces in $M$ that are (almost) transverse to $\phi$. When $\varphi$ has no perfect fits (e.g.…

A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…

Let $C(\mathbf I)$ be the set of all continuous self-maps from ${\mathbf I}=[0,1]$ with the topology of uniformly convergence. A map $f\in C({\mathbf I})$ is called a transitive map if for every pair of non-empty open sets $U,V$ in…

We study moduli spaces $\mathcal{N}$ of rank 2 stable reflexive sheaves on $\mathbb{P}^3$. Fixing Chern classes $c_1$, $c_2$, and summing over $c_3$, we consider the generating function $\mathsf{Z}^{\mathrm{refl}}(q)$ of Euler…