Related papers: Area bound for surfaces in generic gravitational f…

We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We…

The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We…

An analogue model for the $\text{AdS}_2$ spacetime has been recently introduced by Mosna, Pitelli and Richartz [Phys. Rev. D 94, 104065 (2016)] by considering sound waves propagating on a fluid with an ill-defined velocity profile at its…

If $\alpha\in\r$, an $\alpha$-stationary surface in Euclidean space is a surface $\Sigma$ whose mean curvature $H$ satisfies $H(p)=\alpha |p|^{-2} \langle\nu,p\rangle$, $p\in\Sigma$. These surfaces generalize in dimension two a classical…

We prove uniform convergence of metrics $g_k$ on a closed surface with bounded integral curvature (measure) in the sense of A.D. Alexandrov, under the assumption that the curvature measures $\mathbb{K}_{g_k}=\mu^1_k-\mu^2_k$, where…

In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…

Let (M,g) be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset K of M, all volume preserving stable constant mean curvature surfaces of sufficiently large…

In this paper we study curvature types of immersed surfaces in three-dimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff…

We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\kappa}) = {\sigma} over (0,1) with a prescribed asymptotic boundary {\Gamma} at infinity…

In this paper we argue that classical, asymptotically AdS spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each…

We study scalar curvature deformation for asymptotically locally hyperbolic (ALH) manifolds with nonempty compact boundary. We show that the scalar curvature map is locally surjective among either (1) the space of metrics that coincide…

We study minimal Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric whose first normal space is two-dimensional and whose Gauss curvature $K$ and normal curvature $\varkappa$ satisfy the inequality $K^2-\varkappa^2 >0$.…

A lagrangian euclidean model of Drinfeld--Sokolov (DS) reduction leading to general $W$--algebras on a Riemann surface of any genus is presented. The background geometry is given by the DS principal bundle $K$ associated to a complex Lie…

We derive the field equations for topologically massive gravity coupled with the most general quadratic curvature terms using the language of exterior differential forms and a first order constrained variational principle. We find…

In this paper, we investigate the contracting curvature flow of closed, strictly convex axially symmetric hypersurfaces in $\mathbb{R}^{n+1}$ and $\mathbb{S}^{n+1}$ by $\sigma_k^\alpha$, where $\sigma_k$ is the $k$-th elementary symmetric…

We construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces…

We prove that simply connected H-surfaces with bounded area and free boundary in a domain necessarily concentrate at a critical point of the mean curvature of the boundary of this domain.

We investigate the class of ultralocal metrics on the configuration space of canonical gravity. It is described by a parameter $\alpha$, where $\alpha=0.5$ corresponds to general relativity. For $\alpha$ less than a critical value the…

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…

Let $M$ be an $n$-dimensional closed hypersurface with constant mean curvature and constant scalar curvature in an unit sphere. Denote by $H$ and $S$ the mean curvature and the squared length of the second fundamental form respectively. We…