Timeline for Area of distance sphere in manifold with Ricci $\ge 0$.
Current License: CC BY-SA 3.0
10 events
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| Aug 16, 2013 at 23:51 | answer | added | Anton Petrunin | timeline score: 2 | |
| Dec 19, 2011 at 1:15 | comment | added | macbeth | Some evidence in favour: the analogue for horospheres (rather than distance spheres) is true. Specifically, for any Busemann function $b$ on $M$, the area of $b^{-1}(r)$ is eventually nondecreasing in $r$. See Lemma 20 in C. Sormani, "Busemann functions on manifolds with lower bounds on Ricci curvature and minimal volume growth," JDG 1998. (I don't think the theorem's hypothesis of exactly-linear volume growth is needed for this part of the conclusion.) | |
| Oct 9, 2011 at 1:15 | history | edited | user16750 | CC BY-SA 3.0 |
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| Oct 9, 2011 at 0:55 | answer | added | Rbega | timeline score: 1 | |
| Oct 9, 2011 at 0:15 | comment | added | Deane Yang | Don't have time to work out the details, but can't you use the Calabi-Yau lower bound on, say, $V(B(p, 4r))$ and the lower bound on Ricci to infer an isoperimetric inequality on all domains contained in $B(p, 2r)$. That and the Calabi-Yau lower bound on $V(B(p,r))$ implies a lower bound on the area of $\partial B(p,r))$. Not sure how the lower bound depends on $r$ though. | |
| Oct 8, 2011 at 22:42 | comment | added | user16750 | Oh, yes. Thanks Agol, I've corrected my statement | |
| Oct 8, 2011 at 22:40 | history | edited | user16750 | CC BY-SA 3.0 |
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| Oct 8, 2011 at 21:52 | comment | added | Ian Agol | Do you mean for $r$ sufficiently large? | |
| Oct 8, 2011 at 21:37 | history | edited | user16750 | CC BY-SA 3.0 |
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| Oct 8, 2011 at 21:23 | history | asked | user16750 | CC BY-SA 3.0 |