Timeline for Area of distance sphere in manifold with Ricci $\ge 0$.
Current License: CC BY-SA 3.0
5 events
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| Oct 7, 2013 at 1:56 | comment | added | Anton Petrunin | @user3922, Consider the radial map $f\colon W_r\to \partial B_{2r}(q)$. The lower Ricci urvature gives a bound for the $(n-1)$-Jacobian of $f$. It remains to apply the coarea formula. | |
| Oct 6, 2013 at 22:11 | comment | added | J. GE | can you give more detail of how to estimate $W_r$? | |
| Aug 18, 2013 at 21:52 | comment | added | Anton Petrunin | P.S. I realized that there is yet simpler proof. Take a point $q$ on the distance $2{\cdot} r$ from $p$. Denote by $W_r$ the set of all minimizing geodesics from $q$ to the points in $B_\varepsilon(p)$. The standard comparison gives the lower bound on the area of $W_r\cap\partial B_r(p)$. | |
| Aug 17, 2013 at 0:00 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Aug 16, 2013 at 23:51 | history | answered | Anton Petrunin | CC BY-SA 3.0 |