timelike minimal surfaces

Timelike Minimal Surfaces 時間的極小曲面

Lorentz catenoid:

${\sqrt{x^2+y^2}< 2}$ ${\sqrt{x^2+y^2}< 3}$
The conjugate surface of Lorentz catenoid:

${\sqrt{x^2+y^2}< 3}$ ${\sqrt{x^2+y^2}< 4.5}$
"Lorentzian cousin" of Enneper's minimal surface (isothermic):

${\sqrt{x^2+y^2}< 1}$ ${\sqrt{x^2+y^2}< 1.5}$ ${\sqrt{x^2+y^2}< 2}$ ${\sqrt{x^2+y^2}< 2.5}$

${\sqrt{x^2+y^2}< 3}$ ${\sqrt{x^2+y^2}< 4}$ ${\sqrt{x^2+y^2}< 5}$
"Lorentzian cousin" of Enneper's minimal surface (anti-isothermic):

${\sqrt{x^2+y^2}< 1}$ ${\sqrt{x^2+y^2}< 1.5}$ ${\sqrt{x^2+y^2}< 2}$

${\sqrt{x^2+y^2}< 2.5}$ ${\sqrt{x^2+y^2}< 3}$ ${\sqrt{x^2+y^2}< 5}$

References

[1]	J. Inoguchi and M. Toda, Timelike minimal surfaces via loop groups, Acta Appl. Math., 83 (2004), 313-355.

All images were made using Mathematica and JVX files were made using JavaView.

fujimori@math.kobe-u.ac.jp

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