Related papers: Friendly measures, homogeneous flows and singular …

For each irreducible module of the symmetric group on $N$ objects there is a set of parametrized nonsymmetric Jack polynomials in $N$ variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative…

We show that if $\mathcal{L}$ is a line in the plane containing a badly approximable vector, then almost every point in $\mathcal{L}$ does not admit an improvement in Dirichlet's theorem. Our proof relies on a measure classification result…

Explicit Riemannian metrics with Euclidean signature and anti-self dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogenous functions of degree zero in a single real…

The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform…

We study asymptotically harmonic manifolds of negative curvature, without any cocompactness or homogeneity assumption. We show that asymptotic harmonicity provides a lot of information on the asymptotic geometry of these spaces: in…

We consider invariant Riemannian metrics on compact homogeneous spaces $G/H$ where an intermediate subgroup $K$ between $G$ and $H$ exists. In this case, the homogeneous space $G/H$ is the total space of a Riemannian submersion. The metrics…

We study a two-dimensional Navier--Stokes system with anisotropic viscosity, linear damping term, and an additive noise on the whole space $\mathbb{R}^2$. For this model we prove uniqueness of invariant measures when the damping coefficient…

We consider pairs of 3-dimensional Brownian paths, started at the origin and conditioned to have no intersections after time zero. We show that there exists a unique measure on pairs of paths that is invariant under this conditioning, while…

For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence not locally homogeneous. All the local scalar Weyl invariants…

This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of…

It is shown that the characterization of covariant positive operator measures on nonunimodular locally compact groups can be obtained by using vector measure theoretic methods, without an application of Mackey's imprimitivity theorem.

Existence and uniqueness of global in time measure solution for the multidimensional aggregation equation is analyzed. Such a system can be written as a continuity equation with a velocity field computed through a self-consistent…

In this article, we consider the geodesic flow on a compact rank $1$ Riemannian manifold $M$ without focal points, whose universal cover is denoted by $X$. On the ideal boundary $X(\infty)$ of $X$, we show the existence and uniqueness of…

Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…

A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures $\mu$ in $n$-dimensional Euclidean space for all $n\geq 2$ in terms of…

We prove that the space of complete, finite volume, pinched negatively curved Riemannian metrics on a smooth high-dimensional manifold is either empty or it is highly non-connected, provided their behavior at infinity is similar.

In this paper, we consider the cubic nonlinear Schr\"odinger equation with third order dispersion on the circle. In the non-resonant case, we prove that the mean-zero Gaussian measures on Sobolev spaces $H^s(\mathbb{T})$, $s > \frac 34$,…

We prove effective equidistribution of horospherical flows in $\operatorname{SO}(n,1)^\circ / \Gamma$ when $\Gamma$ is geometrically finite and the frame flow is exponentially mixing for the Bowen-Margulis-Sullivan measure. We also discuss…

We define non-pluripolar products of closed positive currents on a compact Kaehler manifold. We show that a positive non-pluripolar measure can be written in a unique way as the top degree self-intersection (in the non-pluripolar sense) of…

Consider a complete Riemannian manifold $(M, g)$ and optimal transport problems on it with cost functions of the form $c(x,y) = h(d_{{g}}(x,y))$. We study the absolute continuity of the corresponding generalized Wasserstein barycenters of…