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Nov 28, 2019 at 17:52 comment added Anton Petrunin In this case you use existence of minimal surface (which is too much for the problem).
Nov 28, 2019 at 14:34 comment added Mohammad Ghomi As you may also know, I think that the moving plane argument here also shows that any minimal surface bounded by $\Gamma$ should be embedded, and therefore orientable, as it will divide $D\times R$ into two regions. So I think that one may assume orientability.
Nov 27, 2019 at 21:54 comment added Anton Petrunin Thank you --- I know how to prove it --- I just wanted a reference. (This should be a classical statement.)
Nov 27, 2019 at 21:26 history edited Mohammad Ghomi CC BY-SA 4.0
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Nov 27, 2019 at 21:12 history answered Mohammad Ghomi CC BY-SA 4.0