Related papers: Gap Eigenvalues and Asymptotic Dynamics of Geometr…

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 introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of…

We prove microlocal estimates at the trapped set of asymptotically Kerr spacetimes: these are spacetimes whose metrics decay inverse polynomially in time to a stationary subextremal Kerr metric. This combines two independent results. The…

We investigate on the existence of smooth complete hypersurface with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under the assumption that there exists an asymptotic subsolution. We give an…

Let $S$ be a punctured Riemann surface with Euler characteristic $\chi(S)<0$. For any unitary representation $\rho: \pi_1(S) \to U(N)$, we introduce its renormalized energy and its harmonic representatives, which are equivariant harmonic…

We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…

The main aim of this paper is to study existence and stability properties of rotationally symmetric proper biharmonic maps between two $m$-dimensional models (in the sense of Greene and Wu). We obtain a complete classification of…

We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains arbitrary large negative eigenvalues and they are simple.…

In this paper, we study transverse linear stability of line solitary waves to the $2$-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in $3$D. In the case where the surface tension is weak or…

For gauge groups SO$(n{+}1)$, SU$(m{+}1)$ and Sp$(\ell{+}1)$, we construct equivariant Yang-Mills solutions on de Sitter space in $n{+}1$, $2(m{+}1)$ and $4(\ell{+}1)$ spacetime dimensions. The latter is conformally mapped to a finite…

In this paper, we present all constant solutions of the Yang-Mills equations with ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space ${\mathbb R}^n$ of arbitrary finite dimension $n$. Using the…

Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…

We study a family of solutions of Einstein-non linear sigma models with $S^2$ and $SU(2) \sim S^3$ target manifolds. In the $S^2$ case, the solutions are smooth everywhere, free of conical singularities, and approach asymptotically the…

We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…

We show that for a given set $\Lambda$ of $nk$ distinct real numbers $\lambda_1, \lambda_2, \ldots, \lambda_{nk}$ and $k$ graphs on $n$ nodes, $G_0, G_1,\ldots,G_{k-1}$, there are real symmetric $n\times n$ matrices $A_s$, $s=0,1,\ldots,…

In this paper we prove the existence of a solution to the Dirichlet problem for harmonic maps into a geodesic ball on which the squared distance function from the origin is strictly convex. This improves a celebrated theorem obtained by S.…

The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly…

In a recent paper [WW23] we studied the transport of oscillations in solutions to linear and some semilinear second-order hyperbolic boundary problems along rays that graze a convex obstacle to any order. We showed that high frequency exact…

In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in a $(n+1)$ dimensional curved space-time, for the cases $n =…

In this paper we consider a semi-linear, defocusing, shifted wave equation on the hyperbolic space \[ \partial_t^2 u - (\Delta_{{\mathbb H}^n} + \rho^2) u = - |u|^{p-1} u, \quad (x,t)\in {\mathbb H}^n \times {\mathbb R}; \] and introduce a…