Timeline for Minimal surfaces + Semi-Geodesic Coordinates
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2014 at 21:21 | comment | added | Robert Bryant | Well, that probably was a bad use of terminology. All I meant to assume was that there is an $\epsilon>0$ such that the map $Z$ that you defined in your question is an injective diffeomorphism on $\Gamma\times (-\epsilon,\epsilon)\subset \Gamma\times\mathbb{R}$. That way, you can be sure that for $t$ sufficiently small, the level sets $\Gamma_t$ are disjoint. I didn't really want to assume anything about the injectivity radius of the induced metric on $\Gamma$. | |
| Nov 29, 2014 at 21:03 | comment | added | Ali | Thanks Robert for your nice answer. May I ask you where the assumption about the positive injectivity radius was used? | |
| Nov 29, 2014 at 14:59 | vote | accept | Ali | ||
| Nov 29, 2014 at 14:22 | history | edited | Robert Bryant | CC BY-SA 3.0 |
added 6 characters in body
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| Nov 29, 2014 at 10:54 | history | answered | Robert Bryant | CC BY-SA 3.0 |