Timeline for When is perimeter continuous under Hausdorff convergence?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 28, 2020 at 20:57 | answer | added | Beni Bogosel | timeline score: 0 | |
| Oct 21, 2020 at 13:28 | comment | added | Leo Moos | My point was that in the situation you describe (with sets that are 'minimal relative perimeter sets') the pathologies listed can (most likely) be avoided altogether, thereby precisely allowing you to avoid writing an argument from scratch. | |
| Oct 21, 2020 at 12:10 | comment | added | Beni Bogosel | @LeoMoos: I was hoping to find some results which prevent me from doing the proof from scratch. It is sure that the sets which interest me are regular (portions of circles/spheres) except some finite (and bounded) number of singular regions. I will look into your advice. | |
| Oct 20, 2020 at 19:51 | history | became hot network question | |||
| Oct 20, 2020 at 15:10 | answer | added | alesia | timeline score: 2 | |
| Oct 20, 2020 at 15:03 | answer | added | Gerald Edgar | timeline score: 4 | |
| Oct 20, 2020 at 14:56 | comment | added | Leo Moos | Have you tried using the results from the compactness and regularity theory for sets with minimising properties? It seems to me that the limit should be regular away from a finite set of points; over the regular portions of the limit surface one ought to be able to apply an Allard regularity theorem for example to deduce the continuity you seek. (Note that this would also exclude the pathological cases you describe.) | |
| S Oct 20, 2020 at 13:19 | history | edited | Beni Bogosel | CC BY-SA 4.0 |
Added top-level tag ("ca.classical-analysis-and-odes" tag excerpt explicitly includes "caclulus of variations")
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| Oct 20, 2020 at 13:00 | review | Suggested edits | |||
| S Oct 20, 2020 at 13:19 | |||||
| Oct 20, 2020 at 12:58 | history | edited | Beni Bogosel | CC BY-SA 4.0 |
added 190 characters in body
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| Oct 20, 2020 at 12:54 | comment | added | Beni Bogosel | @LeoMoos: Sorry, I forgot to mention that. The domains $D_n$ converge to some non degenerate domain $D$ in the Hausdorff metric. They do not necessarily form a monotone sequence. | |
| Oct 20, 2020 at 12:47 | comment | added | Leo Moos | In your problem how do the domains $D_n$ behave for large $n$? Do they converge to some $D$ as $n \to \infty$? Do they form a monotone sequence, perhaps? | |
| Oct 20, 2020 at 11:22 | history | asked | Beni Bogosel | CC BY-SA 4.0 |