Timeline for Submanifolds lying on the boundary of a convex domain
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2011 at 5:53 | comment | added | Bill Thurston | @Andrea Altomani: Good point. I think it depends exactly how you're given the information. If you're told that the function is analytic, it's not enough, as Brouwer-style examples show: e.g. in the plane take the graph of the function $ \Sum(a_i x^{2i})$ where $a_i$ = 1 if the i'th element of an enumeration of all possible formal deductions in some formal system yields the Riemann hypothesis, $a_i = -1$ if the $i$th zero gives a counterexample, and 0 otherwise. It's analytic, but there's no way to know when to stop checking. But more ypically you'd have some other way to understand a curve | |
| Feb 16, 2011 at 19:18 | vote | accept | AndreA | ||
| Feb 16, 2011 at 19:18 | comment | added | AndreA | Thanks for the answer. I still have a question though. Even assuming that we are in a "nice" case (e.g. $M$ is real-analytic) how do i know how many jet spaces i should consider? If for example $M$ contains a straight line, for any order of approximation and any linear functional strict positivity will fail. | |
| Feb 16, 2011 at 1:31 | history | edited | Bill Thurston | CC BY-SA 2.5 |
Fixed blotch where text was missing.
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| Feb 15, 2011 at 18:41 | history | answered | Bill Thurston | CC BY-SA 2.5 |