Related papers: Asymptotic behavior of Cauchy hypersurfaces in con…

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 analyse the stability of black hole Cauchy horizons arising in a class of 2d dilaton gravity models. It is shown that due to the characteristic asymptotic Rindler form of the metric of these models, time dependent…

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…

Based on the $\overline\partial$-generalization of the Deift-Zhou steepest descent method, we extend the long-time and Painlev\'e asymptotics for the Camassa-Holm (CH) equation to the solutions with initial data in a weighted Sobolev space…

In this paper, we present a notion of quasiconvexity in the setting of finitely-generated groups with hyperbolically embedded subgroups. Our main result shows that this notion yields uniform quasiconvex constants in the setting of coned-off…

We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending…

Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…

We consider the Cauchy problem for the generalized Kadomtsev-Petviashvili equations with the dissipation term $-\nu u_{xx}$ in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a spatial anisotropy. In this…

The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by…

Spatially homogeneous models with a scalar field non-minimally coupled to the space-time curvature or to the ordinary matter content are analysed with respect to late-time asymptotic behaviour, in particular to accelerated expansion and…

We study the asymptotic behaviour in time of solutions and the theory of scattering for the modified Schr"odinger map in two space dimensions. We solve the Cauchy problem with large finite initial time, up to infinity in time, and we…

In our model of quantum gravity the quantum development of a Cauchy hypersurface is governed by a wave equation derived as the result of a canonical quantization process. To find physically interesting solutions of the wave equation we…

We address the asymptotic behavior of the $\alpha$-Gauss curvature flow, for $\alpha >1/2$, with initial data a complete non-compact convex hypersurface which is contained in a cylinder of bounded cross section. We show that the flow…

We deal with the large time behavior for a porous medium equation posed in nonhomogeneous media with singular critical density $$ |x|^{-2}\partial_tu(x,t)=\Delta u^m(x,t), \quad (x,t)\in \real^N\times(0,\infty), \ m\geq1, $$ posed in…

Much of our intuition about Effective Field Theories (EFTs) stems from their formulation in flat spacetime, yet EFTs have become indispensable tools in cosmology, where time-dependent backgrounds are the norm. In this work, we demonstrate…

In 2014, Gromov conjectured that sequences of manifolds with nonnegative scalar curvature should have subsequences which converge in some geometric sense to limit spaces with some notion of generalized nonnegative scalar curvature. In…

In this paper, we study large-time asymptotics for heat and fractional heat equations in two discrete settings: the full lattice \(\mathbb Z^d\) and finite connected subgraphs with Dirichlet boundary condition. These results provide a…

We study geodesically complete, singularity free space-times induced by supersymmetric planar domain walls interpolating between Minkowski and anti-de Sitter ($AdS_4$) vacua. A geodesically complete space-time without closed time-like…

We prove the existence of compact surfaces with prescribed constant mean curvature in asymptotically flat and asymptotically hyperbolic manifolds. More precisely, let $(M^3,g)$ be an asymptotically flat manifold with scalar curvature $R\ge…

Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat…