http://lamington.wordpress.com/2009/10/21/schwarz-minimal-surface/ Sun, 14 Apr 2013 21:31:14 +0000 hourly 1 http://wordpress.com/ http://lamington.wordpress.com/2009/10/21/schwarz-minimal-surface/#comment-290 Tue, 29 Jun 2010 17:11:17 +0000 http://lamington.wordpress.com/?p=730#comment-290 The minimal surface shown is a part of the D surface. This was actually explored first by Riemann. Schwarz realised it could be analytically continued to give a 3-periodic version and went on and found the P surface and the H surface. All three are distinct embeddings, though P and D have identical Gauss maps. The links to materials in nature and the lab are many and varied. A third isometric three-periodic minimal surface to the P D family is the Gyroid, discovered by Alan Schoen in the 1960′s. Its existence in E^3 is subtle, but confirmed much later (by Karsten Grosse-Brauckmann, I think). This is probably the most important one for materials science.

]]> http://lamington.wordpress.com/2009/10/21/schwarz-minimal-surface/#comment-269 Fri, 07 May 2010 13:09:13 +0000 http://lamington.wordpress.com/?p=730#comment-269 No, this is the P surface.

]]> http://lamington.wordpress.com/2009/10/21/schwarz-minimal-surface/#comment-268 Fri, 07 May 2010 13:08:41 +0000 http://lamington.wordpress.com/?p=730#comment-268 This is the D surface.

]]> http://lamington.wordpress.com/2009/10/21/schwarz-minimal-surface/#comment-185 Fri, 13 Nov 2009 09:42:00 +0000 http://lamington.wordpress.com/?p=730#comment-185 Great post, thank you!

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