Timeline for On a family of $C^0$-convergent Riemann metrics
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 17, 2012 at 2:17 | comment | added | Anton Petrunin | @Dan. Fix 3 very close points, let $\triangle^\varepsilon$ be geodesic triangles for $g^\varepsilon$ with the vertices at these points. Note that the angles and area of $\triangle^\varepsilon$ converge to the angles and area of $\triangle^0$. Apply Gauss–Bonnet. | |
| May 16, 2012 at 18:31 | comment | added | Dan Lee | @Anton: Perhaps it is obvious, but why does it follow from Gauss-Bonnet in dimension 2? | |
| May 16, 2012 at 12:45 | comment | added | Liviu Nicolaescu | @ Anton: Thanks for the ref. I'll check it out. | |
| May 16, 2012 at 10:26 | comment | added | Anton Petrunin | @Liviu, sorry, it is very cryptic. Look at 4.3 in our "Extremal subsets in ..." and then look at Lemma B.5 in journals.tubitak.gov.tr/math/issues/mat-03-27-1/… . Hope it helps. | |
| May 16, 2012 at 9:35 | comment | added | Liviu Nicolaescu | @ Anton Thank you for your answer. I need to process the strategy that you outlined above. I have to admit that I do not see why $H^\varepsilon$ is smooth and what is the role of the angle condition that you mentioned. | |
| May 16, 2012 at 1:58 | history | answered | Anton Petrunin | CC BY-SA 3.0 |