Helicoidal Maximal Surfaces in Lorentz-Minkowski Space

2003 ◽  
Vol 140 (4) ◽  
pp. 315-334 ◽  
Author(s):  
Pablo Mira ◽  
Jos� A. Pastor
Keyword(s):  
Minkowski Space ◽  
Maximal Surfaces

scholarly journals Periodic maximal surfaces in the Lorentz–Minkowski space $${\mathbb{L}^3}$$

2006 ◽  
Vol 256 (3) ◽  
pp. 573-601 ◽  
Author(s):  
Isabel Fernández ◽  
Francisco J. López
Keyword(s):  
Minkowski Space ◽  
Maximal Surfaces

ON THE GAUSSIAN CURVATURE OF MAXIMAL SURFACES AND THE CALABI–BERNSTEIN THEOREM

2001 ◽  
Vol 33 (4) ◽  
pp. 454-458 ◽  
Author(s):  
LUIS J. ALÍAS ◽  
BENNETT PALMER
Keyword(s):  
Minkowski Space ◽  
Upper Bound ◽  
Gaussian Curvature ◽  
Total Curvature ◽  
Local Geometry ◽  
Maximal Surface ◽  
Bernstein Theorem ◽  
New Approach ◽  
Maximal Surfaces

In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz– Minkowski space L3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L3, involving the local geometry of the surface and its hyperbolic image. As an application of this, a new proof of the Calabi–Bernstein theorem is provided.

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

1991 ◽  
Vol 38 (2) ◽  
Author(s):  
FranciscoJ.M. Estudillo ◽  
Alfonso Romero
Keyword(s):  
Minkowski Space ◽  
Maximal Surfaces

scholarly journals The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 4
Author(s):  
Erhan Güler
Keyword(s):  
Minkowski Space ◽  
Three Dimensional ◽  
Algebraic Surfaces ◽  
Cartesian Coordinates ◽  
Maximal Surfaces ◽  
Dimensional Minkowski Space ◽  
The Family

We consider the Enneper family of real maximal surfaces via Weierstrass data (1,ζm) for ζ∈C, m∈Z≥1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E2,1. Moreover, we propose that the family has degree (2m+1)2 (resp., class 2m(2m+1)) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

Generalized maximal surfaces in Lorentz–Minkowski space L3

1992 ◽  
Vol 111 (3) ◽  
pp. 515-524 ◽  
Author(s):  
Francisco J. M. Estudillo ◽  
Alfonso Romero
Keyword(s):  
Riemann Surface ◽  
Conformal Mapping ◽  
Minkowski Space ◽  
Conformal Structure ◽  
Singular Points ◽  
Maximal Surface ◽  
Branch Points ◽  
Isometric Immersions ◽  
Maximal Surfaces ◽  
Zero Mean Curvature

In this paper we carry out a systematic study of generalized maximal surfaces in Lorentz–Minkowski space L3, with emphasis on their branch points. Roughly speaking, such a surface is given by a conformal mapping from a Riemann surface S in L3. In the last years, several authors [1, 2, 5, 6] have dealt with regular maximal surfaces in L3, i.e. with isometric immersions, with zero mean curvature, of Riemannian 2-manifolds M in L3. So, the term ‘regular’ means free of branch points. As in the minimal case, a conformal structure is naturally induced on M, which becomes a Riemann surface S. The corresponding isometric immersion is then conformal on S, and it does not have any singular points on S (i.e. points on which the differential of the mapping is not one-to-one). This is the way in which generalized maximal surfaces include regular ones. Moreover, branch points are the singular points of the conformal mapping on S. Whereas branch points of generalized minimal surfaces are isolated, we shall show in Section 2 that, in addition to isolated branch points, a generalized maximal surface in L3. may have non-isolated ones, in fact they constitute a 1-dimensional submanifold in a certain open subset of S (see Section 2). So our purpose is two-fold, firstly to study and explain in detail the branch points, and secondly to state several geometric results involving prescribed behaviour of those points on the surface.

On the Gauss curvature of maximal surfaces in the 3-dimensional Lorentz-Minkowski space

1994 ◽  
Vol 69 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Francisco J. M. Estudillo ◽  
Alfonso Romero
Keyword(s):  
Minkowski Space ◽  
Gauss Curvature ◽  
Maximal Surfaces ◽  
3 Dimensional

Björling problem for maximal surfaces in Lorentz–Minkowski space

2003 ◽  
Vol 134 (02) ◽  
pp. 289-316 ◽  
Author(s):  
LUIS J. ALÍAS ◽  
ROSA M. B. CHAVES ◽  
PABLO MIRA
Keyword(s):  
Minkowski Space ◽  
Maximal Surfaces ◽  
Björling Problem
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