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There is a formula for the third variation of area on page 96 of Nitsche's book, Lectures on Minimal Surfaces, vol. 1 (English version). He says at the bottom of the page it is good for normal variations. He gives no calculation at all, just the answer. Has anyone done this calculation? I get an answer that is almost the same but not quite, and can't find my error. Nitsche is very careful so he is probably right, but did anyone else ever do this computation for themselves? Or is there somewhere else in the literature where the third variation formula is presented, independently of Nitsche's computations, so I can cross-check the results?

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    $\begingroup$ Dear @Michael Beeson, it may be helpful to present Nitsche's result and perhaps also your result. That would probably make it easier for anyone trying to answer this question. $\endgroup$
    – Ricardo Andrade
    Mar 30, 2014 at 0:19
  • $\begingroup$ I was not asking people to make this long computation. I am only asking if there is someone out there who, in the course of their own work, has ALREADY done this computation. $\endgroup$
    – Michael Beeson
    Mar 30, 2014 at 4:34
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    $\begingroup$ There's also the possibility that you are both right: that you may just be missing some identity transforming one formula to another. If you post both yours and Nitsche's results, then someone who have not done the full computation can at least check that possibility. $\endgroup$
    – Willie Wong
    Mar 31, 2014 at 7:48

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