scholarly journals Deformation and singularities of maximal surfaces with planar curvature lines

2018 ◽  
Vol 59 (3) ◽  
pp. 465-489 ◽  
Author(s):  
Joseph Cho ◽  
Yuta Ogata
Keyword(s):  
Maximal Surfaces ◽  
Curvature Lines

Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem

Civilizar ◽  
2005 ◽  
Vol 5 (8) ◽  
pp. 63
Author(s):  
Ronaldo A. Garcia
Keyword(s):  
Curvature Lines ◽  
Principal Cycle

In this paper is studied, as a complement of Joachimsthal theorem, the behavior of curvature lines near a principal cycle common to two orthogonal 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

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

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
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