Timeline for Volume of large balls in embedded submanifolds
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Oct 26, 2017 at 17:03 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 26, 2017 at 17:02 | comment | added | Deane Yang | OK. Answer below. | |
| Oct 26, 2017 at 17:01 | vote | accept | Francesco Polizzi | ||
| Oct 26, 2017 at 17:01 | answer | added | Deane Yang | timeline score: 3 | |
| Oct 26, 2017 at 14:24 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
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| Oct 26, 2017 at 14:24 | comment | added | Francesco Polizzi | @Deane Yang: Thank you for the precious information. May I suggest that you expand your comments into an answer, so that the question will not look unanswered anymore? | |
| Oct 26, 2017 at 14:19 | comment | added | Deane Yang | A more general condition is given here: mathoverflow.net/questions/283748/… . Even this condition can probably be weakened more, but there has to be an assumption of "not too much negative Ricci curvature". | |
| Oct 26, 2017 at 12:19 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 25, 2017 at 18:27 | comment | added | Deane Yang | Since volume is an intrinsic geometric invariant, the fact that $M$ is a submanifold is irrelevant. If you assume that Ricci curvature is nonnegative, then the inequality follows from the Bishop-Gromov inequality (in fact, just the Bishop inequality). See en.wikipedia.org/wiki/Bishop%E2%80%93Gromov_inequality | |
| Oct 25, 2017 at 18:19 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Oct 25, 2017 at 18:13 | history | asked | Francesco Polizzi | CC BY-SA 3.0 |