A characterization of quadric constant mean curvature hypersurfaces of spheres

Let $\phi:M\to\mathbb{S}^{n+1}\subset\mathbb{R}^{n+2}$ be an immersion of a complete $n$-dimensional oriented manifold. For any $v\in\mathbb{R}^{n+2}$, let us denote by $\ell_v:M\to\mathbb{R}$ the function given by $\ell_v(x)=\phi(x),v$ and by $f_v:M\to\mathbb{R}$, the function given by $f_v(x)=\nu(x),v$, where $\nu:M\to\mathbb{S}^{n}$ is a Gauss map. We will prove that if $M$ has constant mean curvature, and, for some $v\ne{\bf 0}$ and some real number $\lambda$, we have that $\ell_v=\lambda f_v$, then, $\phi(M)$ is either a totally umbilical sphere or a Clifford hypersurface. As an application, we will use this result to prove that the weak stability index of any compact constant mean curvature hypersurface $M^n$ in $\mathbb{S}^{n+1}$ which is neither totally umbilical nor a Clifford hypersurface and has constant scalar curvature is greater than or equal to $2n+4$.Comment: Final version (February 2008). To appear in the Journal of Geometric Analysi

Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson-Walker spacetimes

In this paper we analyze the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing some previous results given in [2]. We next extend these results to the complete noncompact case. In that case, our approach is based on the use of a generalized version of the Omori-Yau maximum principle for trace type differential operators, recently given in [3].Comment: To appear in Mathematical Proceedings of the Cambridge Philosophical Societ

Conformal Kaehler submanifolds

This paper presents two results in the realm of conformal Kaehler submanifolds. These are conformal immersions of Kaehler manifolds into the standard flat Euclidean space. The proofs are obtained by making a rather strong use of several facts and techniques developed by S. Chion and M. Dajczer for the study of isometric immersions of Kaehler manifolds into the standard hyperbolic space

Comparison theory of Lorentzian distance with applications to spacelike hypersurfaces

In this paper we summarize some comparison results for the Lorentzian distance function in spacetimes, with applications to the study of the geometric analysis of the Lorentzian distance on spacelike hypersurfaces. In particular, we will consider spacelike hypersufaces whose image under the immersion is bounded in the ambient spacetime and derive sharp estimates for the mean curvature of such hypersurfaces under appropriate hypotheses on the curvature of the ambient spacetime. The results in this paper are part of our recent work [1], where complete details and further related results may be found

La confabulación de Gilles Deleuze y Félix Guattari: escritura literaria contra flujos de poder

En este artículo se ponen en relación las concepciones de filosofía, literatura y poder con las que Gilles Deleuze y Félix Guattari crearon su particular modo de pensamiento. así  es como, en contra de una hegemonía que se  extiende desde el logos hasta el signo lingüístico, la literatura supondría, en algunos casos concretos de la literatura universal, un espacio político capaz de cuestionar el establecimiento de la historia oficial por medio de la ficción tantas veces subestimada.Cet article met en rapport les conceptions de philosophie, littérature et pouvoir avec lesquelles Gilles Deleuze et Félix Guattari ont créé leur particulier mode de pensée. C’est ainsi que, contre une hégémonie qui s’étend depuis le logos jusqu’au signe linguistique, la littérature suppose que, dans quelques cas concrets de la littérature universelle, un espace politique capable de remettre en question l’établisement de l’histoire officielle grâce à la fiction très souvent sous-estimée.This article connect the conceptions of philosophy, literature and power with the conceptions with ones Gilles Deleuze and Félix Guattari created their particular way of thinking. like  this, against the hegemony that  extends from the logos until the linguishe sign, the literature would suppose, in some concrete cases of the universal literature, a politic space able to question the official history through fiction so many times undirestimated

Spacelike surfaces with free boundary in the Lorentz-Minkowski space

We investigate a variational problem in the Lorentz-Minkowski space \l^3 whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of spacelike hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space \l^{n+1}.Comment: 16 pages. Accepted in Classical and Quantum Gravit

Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory

We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting of a pulse in the antisymmetric field variable. We demonstrate that marginally trapped surfaces do exist for this choice of initial data.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 3 pages, 1 figur

The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page