Timeline for Question about a particular estimate in Riemannian geometry
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 15, 2014 at 16:36 | comment | added | José Carlos | @DeaneYang Thank you for your patience and advices. | |
| Jul 14, 2014 at 16:22 | comment | added | Deane Yang | Unfortunately, I haven't looked carefully at more recent publications, but this book by Hebey looks perfect: amazon.com/dp/0821827006/ref=rdr_ext_tmb | |
| Jul 14, 2014 at 16:20 | comment | added | Deane Yang | This depends on what exactly you need to know, and that depends on what you need the Sobolev spaces for. Could you say more about the context where you need them? | |
| Jul 14, 2014 at 15:00 | comment | added | José Carlos | @DeaneYang, thank you. It is so difficult to study the book of Aubin. I really need to learn about Sobolev spaces on manifolds. Do you know a "better" book to study about it? Thanks. | |
| Jul 14, 2014 at 3:56 | comment | added | Deane Yang | José, thanks. And I apologize. I should have remembered that Aubin wrote this a long time ago and used local co-ordinates and brute force in his proofs. Theorem 1.53 is awful. There are much easier ways to prove the inequality using Jacobi fields. I recommend reading the appendices of Karcher, Riemannian center of mass and mollifier smoothing. Comm. Pure Appl. Math. 30 (1977), no. 5, 509–541, as well as math.uni-augsburg.de/~eschenbu/comparison.pdf. | |
| Jul 14, 2014 at 1:07 | comment | added | José Carlos | @DeaneYang I re-wrote the question!! | |
| Jul 14, 2014 at 0:59 | history | edited | José Carlos | CC BY-SA 3.0 |
added 1925 characters in body
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| Jul 13, 2014 at 19:35 | comment | added | Deane Yang | I think the definition of each constant (for example, $-a$ is presumably the lower bound of the sectional curvature and $\delta$ the diameter of $\tilde{B}$) plus the statement of Theorem 1.53 will be enough. To be honest, I can probably figure out what everything is but you really should state your question so that anyone can read and understand the question and answer without having to consult the book. | |
| Jul 13, 2014 at 16:11 | comment | added | José Carlos | I will write the theorem 1.53 here and will try to explain the notations. However, we need a lot of definitions and notations of this book to understand my doubt. Unfortunatly, the own notation is confusing. Anyway, I will write it later. Thank you. | |
| Jul 13, 2014 at 5:29 | comment | added | Deane Yang | There's nothing wrong with citing the book, but your question assumes that we know what Theorem 1.53, $\nabla_E$, $dE$, $a$, $\delta$ are. But if we don't have the book, we don't. All you need to do is say what these are. | |
| Jul 13, 2014 at 2:31 | comment | added | José Carlos | I cited the book because he explain that this is a consequence of a theorem. This inequality is a step of a proof, which he uses another result to obtain it. If I had wrote here, would be confusing. The reference is necessary to understand it. | |
| Jul 12, 2014 at 2:00 | review | Close votes | |||
| Jul 13, 2014 at 16:51 | |||||
| Jul 12, 2014 at 1:54 | comment | added | Deane Yang | You're more likely to get an answer if your question is self-contained instead of citing page and theorem numbers from a book that we might not own. | |
| Jul 12, 2014 at 0:20 | history | asked | José Carlos | CC BY-SA 3.0 |