Maximal surfaces with singularities in Minkowski space

By Masaaki Umehara, Kotaro Yamada. 2003

154 citations recorded by the source corpus.

We shall investigate maximal surfaces in Minkowski 3-space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal surfaces with singularities and we show that they satisfy an Osserman-type inequality.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/4e9c44c6d870e173aa658d8e9eee17c001aeea81

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Kentaro Saji
2. Masaaki Umehara
3. Kotaro Yamada
4. I. Fernández
5. Rabah Souam
6. Pablo Mira
7. Benoît Daniel

In Astronomy and Astrophysics

1. I. Fernández
2. Rabah Souam

Citations in the corpus

• The geometry of fronts (2005, background): “([ UY ]), and via constant mean curvature one surfaces in de Sitter space ([F], see also Lee and Yang [LY]).”
• Flat surfaces with singularities in Euclidean 3-space (2006, unknown): “Finally, we mention several related works: [7] for flat fronts in S(3); [25], [6] for behaviour of the Gaussian curvature near cuspidal edges, swallowtails, and cuspidal cross caps; [29], [17], [4], [5],[18] for singularity of spacelike maximal surfaces in R(3)1 and CMC-1 surfaces in de Sitter 3-spa”
• The space of complete embedded maximal surfaces with isolated singularities in the 3-dimensional Lorentz-Minkowski space (2003, background): “From a different point of view, Umehara and Yamada [ 23 ] have proved some results about the global behavior of maximal immersed surfaces in L 3 with analytical curves of singularities.”