相关论文: Ground state solution for a problem with mean curv…

The classical Minkowski problem in Minkowski space asks, for a positive function $\phi$ on $\mathbb{H}^d$, for a convex set $K$ in Minkowski space with $C^2$ space-like boundary $S$, such that $\phi(\eta)^{-1}$ is the Gauss--Kronecker…

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the…

We consider a simple cavity optomechanics and study the ground-state cooling of mechanical resonator in the quantum regime. Using the effective master equations in the linear regime, the equations of motion can be obtained for the second…

In the framework of the nonlinear stability of Minkowski spacetime, we show that if the radiation field of the curvature tensor vanishes, the spacetime must be flat.

We study the non-linear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish…

We prove a Minkowski type inequality for weakly mean convex and star-shaped hypersurfaces in warped cylinders which are asymptotically flat or hyperbolic. In particular, we show that this sharp inequality holds for outward minimizing…

In this paper, we study the anisotropic Minkowski problem. It is a problem of prescribing the anisotropic Gauss-Kronecker curvature for a closed strongly convex hypersurface in Euclidean space as a function on its anisotropic normals in…

The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on round spheres. In this paper we employ a locally constrained…

We consider the problem $F=f(\nu)$ for strictly convex, closed hypersurfaces in hyperbolic space and solve it for curvature functions $F$ the inverses of which are of class $(K^*)$.

We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $D \ge 4$. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution $W$, called…

An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference…

In the Minkowski space, we consider a compact, spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane…

In this work, we study spacelike surfaces in Minkowski space $E_1^3$ foliated by pieces of circles and that satisfy a linear Weingarten condition of type $a H+b K=c$, where $a,b$ and $c$ are constant and $H$ and $K$ denote the mean…

This paper deals with the prescribed mean curvature equations both in the Euclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity $g$ such that $g'(0)>0$. We show the existence of oscillating solutions, namely with an…

In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is $0$…

The paper concerns the existence of normalized solutions to a large class of quasilinear problems, including the well-known Born-Infeld operator. In the mass subcritical cases, we study a global minimization problem and obtain a ground…

The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…

This paper concerns the existence and related properties of solutions to the Schr\"{o}dinger-Bopp-Podolsky system, which reduces to a nonlinear and nonlocal partial differential equation describing a Schr\"{o}dinger field coupled with its…

Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical…

We obtain a gradient estimate for the Gauss maps from complete spacelike constant mean curvature hypersurfaces in Minkowski space into the hyperbolic space. As applications, we prove a Bernstein theorem which says that if the image of the…