Timeline for Volumes of convex vs non-convex polyhedra with prescribed facets areas
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2013 at 20:52 | vote | accept | Pietro Dona' | ||
| Jul 10, 2013 at 9:49 | answer | added | hexe7 | timeline score: 3 | |
| Jul 7, 2013 at 6:18 | comment | added | Igor Pak | There is in fact an extension of Minkowski thm to non-convex polyhedra. See G.Y. Panina tinyurl.com/n9cpbvy (MR1970337) and V. Alexandrov arxiv.org/pdf/math/0211286v1.pdf This does not really answer your question, but suggests a possibility that the claim might be false. | |
| Jul 5, 2013 at 15:27 | comment | added | Ian Agol | One could ask a more general question. Consider a measure on $S^2$, and suppose this is the push-forward of the area measure of a surface in $R^3$ under the Gauss map. Then one can ask whether a convex surface realizing this Gauss map measure will have larger volume than a non-convex surface with the same Gauss map measure. | |
| Jul 5, 2013 at 3:13 | answer | added | Igor Rivin | timeline score: -1 | |
| S Jul 5, 2013 at 0:03 | history | edited | Igor Pak |
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| Jul 5, 2013 at 0:03 | review | Suggested edits | |||
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| Jul 4, 2013 at 12:53 | review | First posts | |||
| Jul 4, 2013 at 13:36 | |||||
| Jul 4, 2013 at 12:44 | history | edited | Pietro Dona' | CC BY-SA 3.0 |
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| Jul 4, 2013 at 12:37 | history | asked | Pietro Dona' | CC BY-SA 3.0 |