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For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined by the dimension of the trapped set. This covers the case of…

We investigate when plane-wave memory admits standard outgoing free data beyond the idealized sandwich-wave approximation. For a Brinkmann plane wave with profile $A(U)$, the commonly used condition $A(U)|_{U\to\infty}=0$ is not sufficient…

Let $X_t$ be the (reflecting) diffusion process generated by $L:=\Delta+\nabla V$ on a complete connected Riemannian manifold $M$ possibly with a boundary $\partial M$, where $V\in C^1(M)$ such that $\mu(d x):= e^{V(x)}d x$ is a probability…

Let $M$ be a pinched negatively curved Riemannian manifold, whose unit tangent bundle is endowed with a Gibbs measure $m_F$ associated to a potential $F$. We compute the Hausdorff dimension of the conditional measures of $m_F$. We study the…

We prove the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, both with Lipschitz-continuous and with polynomial…

Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…

For a unit vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$, $n\geq 1$, we exhibit a nontrivial lower bound for its energy which depends on the degree of the Gauss map of the immersion. When the hypersurface is the unit…

The Teichm\"uller harmonic map flow deforms both a map from an oriented closed surface $M$ into an arbitrary closed Riemannian manifold, and a constant curvature metric on $M$, so as to reduce the energy of the map as quickly as possible…

The metric for plane gravitational waves is quantized using the Ashtekar field variables. The z axis (direction of travel of the waves) is taken to be the entire real line. Solutions to the constraints are proposed; they involve open-ended…

We obtain a lower bound for the amplitude of nonzero homoclinic traveling wave solutions of the McKenna--Walter suspension bridge model. As a consequence of our lower bound, all nonzero homoclinic traveling waves become unbounded as their…

We study Gamma-convergence of graph based Ginzburg-Landau functionals, both the limit for zero diffusive interface parameter epsilon->0 and the limit for infinite nodes in the graph m -> infinity. For general graphs we prove that in the…

This article addresses a fundamental concern regarding the incompressible approximation of fluid motions, one of the most widely used approximations in fluid mechanics. Common belief is that its accuracy is $O(\epsilon)$ where $\epsilon$…

We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a…

In the present paper we prove that the pipe Poiseuille flow of parabolic velocity profile attenuates exponentially in time with respect to three dimensional infinitesimal disturbances at all finite wave numbers and Reynolds numbers for…

In this paper escape rates and local escape rates for special flows are sudied. In a general context the first result is that the escape rate depends monotonically on the ceiling function and fulfills certain scaling, invariance, and…

We consider Gaussian random waves on hyperbolic spaces and establish variance asymptotics and central limit theorems for a large class of their integral functionals, both in the high-frequency and large domain limits. Our strategy of proof…

We study the motion of sets by anisotropic curvature under a volume constraint in the plane. We establish the exponential convergence of the area-preserving anisotropic flat flow to a disjoint union of Wulff shapes of equal area, the…

We study large traveling surface waves within a two-dimensional finite depth, free boundary, homogeneous, incompressible and viscous fluid governed by Darcy's law. The fluid is bound by a gravitational force to a flat rigid bottom and meets…

We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment…

Physical experiments show that a capillary water jet is exponentially unstable under long wave perturbations, while remaining stable under short wave perturbations. Measurements indicate that the exponential growth rate in the long wave…