Timeline for Does pseudo-holomorphic *submanifolds* satisfy unique continuation?
Current License: CC BY-SA 3.0
13 events
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| Sep 4, 2015 at 15:44 | history | edited | Nikolaki | CC BY-SA 3.0 |
Added a Remark concerning the genericity of the proposed partial solution. As well, as a clarification that the answer is partial.
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| Sep 4, 2015 at 10:58 | comment | added | Nikolaki | Sorry, my previous approach was clearly incorrect. Is my new proposal general enough for you? | |
| Sep 4, 2015 at 10:56 | history | edited | Nikolaki | CC BY-SA 3.0 |
Added an approach to the general case.
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| Sep 4, 2015 at 10:23 | history | edited | Nikolaki | CC BY-SA 3.0 |
Removed a faulty proof of the general case.
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| Sep 4, 2015 at 10:06 | comment | added | John Pardon | I don't understand. As you remarked before, the answer is clearly "no" if we omit the hypothesis $f=g\circ\phi$. Now you claim the answer is "yes", but your argument does not use the fact that $f=g\circ\phi$. Note that $\phi$ need not send your disks with analytic boundary to other disks with analytic boundary. | |
| Sep 4, 2015 at 9:59 | history | edited | Nikolaki | CC BY-SA 3.0 |
The previous partial answer has (hopefully) been completed. The previous provided (counter) example was irrelevant to the question and has been removed.
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| Sep 4, 2015 at 9:25 | comment | added | Nikolaki | Of course, you are right. Let me try to fix it by applying the application I had in mind, hopefully it will work... | |
| Sep 4, 2015 at 9:17 | comment | added | John Pardon | Why is the answer no in general? I think you are missing the hypothesis that $f=g\circ\phi$ (which is really the crux of the question). | |
| Sep 4, 2015 at 9:11 | comment | added | Nikolaki | I agree. Hopefully the new answer gives the complete picture for your question. For the applications, I would imagine that you can get away by assuming a real analytic boundary (cover your Riemann surface with small analytic discs). But OK, here I'm just guessing what applications you have in mind. | |
| Sep 4, 2015 at 9:09 | history | edited | Nikolaki | CC BY-SA 3.0 |
Tried to rephrase the answer given the more general question.
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| Sep 4, 2015 at 9:00 | history | edited | Nikolaki | CC BY-SA 3.0 |
Tried to rephrase the answer given the more general question.
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| Sep 4, 2015 at 8:59 | comment | added | John Pardon | Indeed, the question was sort of trivial as I originally phrased it. I've now modified it to be nontrivial. | |
| Sep 4, 2015 at 7:57 | history | answered | Nikolaki | CC BY-SA 3.0 |