On maximal surfaces in the n-dimensional Lorentz-Minkowski space

Estudillo, Francisco J. M.; Romero, Alfonso

doi:10.1007/bf00181216

Cited by 20 publications

(40 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a corollary of this result, we give a simple new proof of the Calabi-Bernstein theorem ([4], [7]) for maximal space-like surfaces in R 3 1 from the viewpoint of value-distributiontheoretic properties of the Lorentzian Gauss map. We remark that Alías and Palmer [2], Estudillo and Romero [8,9,10], Osamu Kobayashi [20], Romero [32] and Umehara and Yamada [36] have approached this theorem from other viewpoints. Proof.…”

Section: Lorentzian Gauss Map Of Maxfaces In the Lorentz-minkowski 3-mentioning

confidence: 99%

On the maximal number of exceptional values of Gauss maps for various classes of surfaces

Kawakami

2012

Math. Z.

View full text Add to dashboard Cite

The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and weakly complete flat surfaces in the hyperbolic three-space. For this purpose, we give an effective curvature bound for a specified conformal metric on an open Riemann surface.2010 Mathematics Subject Classification. Primary 30D35, 53C42 ; Secondary 30F45, 53A10, 53A15.

show abstract

Section: Lorentzian Gauss Map Of Maxfaces In the Lorentz-minkowski 3-mentioning

confidence: 99%

On the maximal number of exceptional values of Gauss maps for various classes of surfaces

Kawakami

2012

Math. Z.

View full text Add to dashboard Cite

show abstract

“…We shall now attempt to capitalize on the facts that maximal hypersurfaces have received much attention in the general relativity and differential geometry literature [16,17,20,24,37,39,45] and Born-Infeld electrostatics was extensively studied in the 1930's [5,21] to obtain some insight into both topics by exploiting this connection. The first obvious point is that one may use the Poincaré symmetries of the maximal hypersurface problem in d + 1 diimensional Minkowski spacetime to generate some useful new solutions of the electrostatic problem.…”

Section: Electrostatic Solutions and Maximal Hypersurfacesmentioning

confidence: 99%

Born-Infeld particles and Dirichlet p-branes

1998

View full text Add to dashboard Cite

Born-Infeld theory admits finite energy point particle solutions with δ-function sources, BIons. I discuss their role in the theory of Dirichlet p-branes as the ends of strings intersecting the brane when the effects of gravity are ignored. There are also topologically non-trivial electrically neutral catenoidal solutions looking like two p-branes joined by a throat. The general solution is a non-singular deformation of the catenoid if the charge is not too large and a singular deformation of the BIon solution for charges above that limit. The intermediate solution is BPS and Coulomblike. Performing a duality rotation we obtain monopole solutions, the BPS limit being a solution of the abelian Bogolmol'nyi equations. The situation closely resembles that of sub and super extreme black-brane solutions of the supergravity theories. I also show that certain special Lagrangian submanifolds of C p , p = 3, 4, 5, may be regarded as supersymmetric configurations consisting of p-branes at angles joined by throats which are the sources of global monopoles. Vortex solutions are also exhibited.

show abstract

“…When the ambient space is the Lorentz-Minkowski space L 3 , maximal surfaces share a certain type of geometric properties with minimal surfaces in Euclidean space E 3 . For instance, maximal surfaces represent a maximum for the area integral [3], and they also admit an Enneper-Weierstrass representation [6,7,14].…”

Section: Introductionmentioning

confidence: 99%

Björling problem for maximal surfaces in Lorentz–Minkowski space

Alı́as

Chaves

Mira

2003

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

We introduce a new approach to the local study of maximal surfaces in Lorentz-Minkowski space, based on a complex representation formula for this kind of surfaces. As an application we solve a certain Björling-type problem in Lorentz-Minkowski space and we obtain some results related to it. We also establish, springing from this complex representation, a way of introducing examples of maximal surfaces with interesting prescribed geometric properties. Further applications of the complex representation let us inspect some known results from a different perspective, and show how our approach can be used to classify certain families of maximal surfaces. † Partially supported by Dirección General de Investigación (MCYT) BFM2001-2871 and Consejería de Educación y Universidades (CARM) Programa Séneca, PI-3/00854/FS/01.

show abstract

On maximal surfaces in the n-dimensional Lorentz-Minkowski space

Abstract: Complete maximal surfaces in the n-dimensional Lorentz-Minkowski space are studied from the behaviour of their normal vectors. Moreover, several examples of maximal surfaces are constructed.

Cited by 20 publications

References 9 publications

On the maximal number of exceptional values of Gauss maps for various classes of surfaces

On the maximal number of exceptional values of Gauss maps for various classes of surfaces

Born-Infeld particles and Dirichlet p-branes

Björling problem for maximal surfaces in Lorentz–Minkowski space

Contact Info

Product

Resources

About