Timeline for How many minimal surfaces do we have if the metric in the target space is not flat
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| S Aug 30, 2023 at 4:34 | history | suggested | Ali Taghavi |
two tags are added
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| Aug 29, 2023 at 20:19 | review | Suggested edits | |||
| S Aug 30, 2023 at 4:34 | |||||
| Dec 18, 2015 at 11:10 | vote | accept | Vladimir S Matveev | ||
| Dec 16, 2015 at 14:11 | comment | added | Robert Bryant | What Ben is referring to is the fact (originally proved by Bekkar, though I have a different proof) that the space of metrics on $\mathbb{R}^3$ for which all the planes are minimal surfaces has dimension 20. This is interesting because the space of metrics defined on a neighborhood of $0\in\mathbb{R}^3$ that are projectively equivalent to the standard flat metric is only $9$ dimensional. | |
| Dec 16, 2015 at 14:06 | answer | added | Robert Bryant | timeline score: 5 | |
| Dec 16, 2015 at 13:42 | comment | added | Ben McKay | It is interesting to fix a metric, take a minimal surface through each point tangent to each 2-plane, and then try to change metrics while keeping that family of surfaces minimal. Robert Bryant has results on this question for the standard metric on Euclidean space. | |
| Dec 16, 2015 at 13:04 | answer | added | Igor Rivin | timeline score: 2 | |
| Dec 16, 2015 at 12:57 | history | asked | Vladimir S Matveev | CC BY-SA 3.0 |