Timeline for minimal surfaces in $S^n$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 7, 2016 at 21:16 | comment | added | Arctic Char | @Paul If you treat the minimal surfaces as conformal harmonic mappings, that there is no neck and no energy loss follows from the fact that the mapping are conformal. | |
| Jun 7, 2016 at 11:26 | comment | added | Otis Chodosh | Hi Paul, the "varifold statement" is essentially a beefed up version of the fact that Radon measures (think of the Hausdorff measure restricted to $\Sigma_j$ with uniform mass bounds admit a convergent subsequence to some measure (the measure has no structure, a priori). No area can be bubbled off (essentially, because area is a subcritical quantity). Another way to see this is via the monotonicity formula: if a minimal surface concentrates a lot of area in a small region, then its overall area must be really huge. | |
| Jun 7, 2016 at 11:11 | vote | accept | Paul | ||
| Jun 7, 2016 at 11:11 | comment | added | Paul | @ Otis, Thank you very much for the counter example. For your last remark, I image that the limit object can be singular?I mean, a priori you can converge to a union of smooth and singular mesure, no? To be more precise, is that know that there is a no neck energy property in the bubbling process? | |
| Jun 7, 2016 at 7:58 | history | edited | Otis Chodosh | CC BY-SA 3.0 |
fixed sign error
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| Jun 6, 2016 at 15:10 | history | answered | Otis Chodosh | CC BY-SA 3.0 |