Timeline for Ball-Box Theorem and Sequence of Distributions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 28, 2013 at 9:54 | comment | added | Avicenna | 4- Finally the part about trying to say whether if there exists a uniform constant c s.t ck>c for all k depends on the oscillation property of ([ek,gk],fk) right? So for instance as in my first question i.) if you assume it is uniformly bounded below but not going to zero as in ii.) then such a c exists? Thanks alot again. | |
| Jun 28, 2013 at 9:32 | vote | accept | Avicenna | ||
| Oct 10, 2013 at 15:39 | |||||
| Jun 28, 2013 at 9:31 | comment | added | Avicenna | 2- Is it vaguely true that the relation of the constants with maximum and minimum of $([e^k,g^k],f^k)$ somehow comes from the fact that (since e,g,f are orth) $([e^k,g^k],f^k) = df(e^k,g^k)$ and $df^k$ can be integrated over certain area pieces to get estimates about the length of the sR geodesics. 3- Suppose you only know that $([e,g],f)$ goes to 0 and that the surface $x\circ exp(te^k,sg^k)$ converges to a hypersurface for $t,s<T$. Then the ball box theorem states that $B_{sR}(x,T)$ and the orbit of x for all time less than T also converge in $C^0$ manner to that hypersurface? | |
| Jun 28, 2013 at 9:12 | comment | added | Avicenna | Thanks alot, reflecting on your answer clarified some misunderstandings I had in my mind. However I have some more questions: $$ 1- Does the arguement rely on the fact that this 3 dimensional, it seems that the key point is that the distribution is codimension 1. Is it in the last part where 3d becomes important? | |
| Jun 27, 2013 at 15:37 | history | answered | Sergei Ivanov | CC BY-SA 3.0 |