Timeline for Bounds on functions pullbacked via exponential map
Current License: CC BY-SA 3.0
5 events
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| May 14, 2014 at 21:51 | comment | added | Deane Yang | Thanks but I don't consider what I wrote to be an answer. It's a guess about how to get a possible answer. If you figure it all out, you could, if you want, post an answer yourself. | |
| May 14, 2014 at 14:20 | comment | added | Matthias Ludewig | Sounds good, I will look into that! You should probably post this as an answer so I can accept it! | |
| May 14, 2014 at 3:55 | comment | added | Deane Yang | I haven't worked this out carefully but doesn't assuming nonnegative sectional curvature and bounded covariant derivatives of order 1 and higher give you what you want? Basically, for the bound on the first derivative you need the Jacobi fields to grow slower than the ones for the flat metric. To get bounds for the higher derivatives, you have to control the inhomogeneous term of the differentiated Jacobi equation. Bounded covariant derivatives of the curvature tensor should accomplish that. | |
| May 13, 2014 at 21:11 | history | edited | Matthias Ludewig |
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| May 13, 2014 at 12:28 | history | asked | Matthias Ludewig | CC BY-SA 3.0 |