Where can I find the result that states that the minimal surfaces immersed in $\mathbb{R}^3$ are of revolution?

I was searching the internet but I do not think so.


closed as off-topic by Will Jagy, Chris Custer, trancelocation, user99914, Strants May 15 '18 at 13:04

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  • 1
    $\begingroup$ this is false as stated. There are plenty of immersed, sometimes embedded, minimal surfaces in $\mathbb R^3$ $\endgroup$ – Will Jagy May 15 '18 at 0:22
  • $\begingroup$ And what is the correct statement? $\endgroup$ – Mancala May 15 '18 at 0:26
  • $\begingroup$ Where did you see this assertion? If you provide the reference it might be easier to see what are referring to. $\endgroup$ – user99914 May 15 '18 at 0:36
  • $\begingroup$ It was in the abstract of this article: arxiv.org/pdf/0804.4211.pdf I think I already found it, it looks like Schoen's Theorem $\endgroup$ – Mancala May 15 '18 at 0:43
  • $\begingroup$ Surfaces of revolution are easier to calculate and visualize. Non axisymmetric CMC surfaces can be physically realized by taking any closed loop and blowing air on one side to create constant pressure $p$ across a soap film of surface tension $T$ as it obeys the law for 2D surface with differential eqation $ \kappa_1+ \kappa_2 = p/T $ contained in $\mathbb R^3$. $\endgroup$ – Narasimham May 15 '18 at 1:53