Timeline for Does the R-sphere condition imply that a surface is locally a graph of function on a ball of radius R?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2014 at 13:24 | vote | accept | pedro | ||
| May 17, 2014 at 13:20 | comment | added | pedro | I think that once we have that $\cos\theta+\frac{|v|^2}2\ge 1$, then can conclude easily by using that $$|v|^2 \leq |x|^2 + (1-\sqrt{1-|x|^2})^2,$$ for $|x|\leq1$, which follows by writing the touching spheres at $O$. Indeed we find that $\cos\theta \geq \sqrt{1-|x|^2}$ and we conclude. Thank you again for your answer! | |
| May 16, 2014 at 17:57 | history | answered | fedja | CC BY-SA 3.0 |