Luis José Alías Linares

Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes

In this paper we study the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson�Walker (GRW) spacetimes. In particular, we consider the following question: under what conditions must a compact spacelike hypersurface with constant higher order mean curvature in a spatially closed GRW spacetime be a spacelike slice? We prove that this happens, essentially, under the so called null convergence condition. Our approach is based on the use of the Newton transformations (and their associated differential operators) and the Minkowski formulae for spacelike hypersurfaces.

Uniqueness of constant mean curvature surfaces properly immersed in a slab

We study complete properly immersed surfaces contained in a slab of a warped product

An estimate for the sectional curvature of cylindricalli bounded submanifolds

\mathbb{R}\times_\varrho\mathbb{P}^2

On the area of constant mean curvature discs and annuli with circular boundaries

, where

On the stability index of minimal and constant mean curvature hypersurfaces in spheres

\mathbb{P}^2

A mean curvature estimate for cylindrically bounded submanifolds

is complete with nonnegative Gaussian curvature. Under certain restrictions on the mean curvature of the surface we show that such an immersion does not exists or must be a leaf of the trivial totally umbilical foliation

Análisis geométrico y geometría global de superficies : una introducción elemental

t \in \mathbb{R}\mapsto \{t\} \times \mathbb{P}^2

Spacelike hypersurfaces with constant mean curvature in the steady state space

We give sharp sectional curvature estimates for complete immersed cylindrically bounded m-submanifolds φ : M → N × Rl, n+ l ≤ 2m− 1 provided that either φ is proper with the second fundamental form with certain controlled growth or M has scalar curvature with strong quadratic decay. This latter gives a non-trivial extension of the Jorge-Koutrofiotis Theorem [8]. Mathematics Subject Classification (2000): 53C42

Proceedings of XIII Fall Workshop on Geometry and Physics : Murcia, Spain, september 20-22, 2004

Abstract. It is still an open question whether a constant mean curvature (CMC) disc which is bounded by a circle is necessarily a spherical cap or a flat disc. The authors together with López [1] recently showed that the only stable CMC discs which are bounded by a circle are spherical caps. In this paper we derive lower bounds for the area of constant mean curvature discs and annuli with circular boundaries in 3-dimensional space forms.