相关论文: Perturbative solutions to the extended constant sc…

We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically…

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of…

We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology…

We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the equations,…

This article concerns a natural generalization of the classical asymptotic Plateau problem in hyperbolic space. We prove the existence of a smooth complete hypersurface of constant scalar curvature with a prescribed asymptotic boundary at…

We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict…

We study expansions near the boundary of solutions to the Dirichlet problem for the constant mean curvature equation in the hyperbolic space. With a characterization of remainders of the expansion by multiple integrals, we establish optimal…

We prove local in time Strichartz estimates without loss for the restriction of the solution of the Schroedinger equation, outside a large compact set, on a class of asymptotically hyperbolic manifolds.

We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an…

An asymptotic expansion with respect to a small parameter of a singularly perturbed system of hyperbolic equations, describing vibrations of two rigidly connected strings is constructed. Under certain conditions imposed on these problems,…

We consider surfaces of constant Gaussian curvature immersed in 3-dimensional manifolds, and we strengthen the compactness result of Labourie in the case where the ambient manifold is 3-dimensional hyperbolic space. This allows us to prove…

In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations for two dimensional incompressible fluid with constant…

Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply…

The existence of a smooth complete strictly locally convex hypersurface with prescribed scalar curvature and asymptotic boundary at infinity in $\mathbb{H}^{3}$ is proved under the assumption that there exists a strictly locally convex…

In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have…

The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy…

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…

Let $(M,\,g)$ be a Poincar$\acute{\text{e}}$-Einstein manifold with a smooth defining function. In this note, we prove that there are infinitely many asymptotically hyperbolic metrics with constant $Q$-curvature in the conformal class of an…

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.

We investigate the problem of finding complete strictly convex hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of curvature functions.