Timeline for Epsilon regularity for minimal surfaces in arbitrary Riemannian manifolds
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2016 at 15:30 | vote | accept | Andy Sanders | ||
| Feb 24, 2016 at 19:58 | comment | added | Rbega | The point being that to prove something like 1) it suffices to do most of your work in euclidean space as that is what the Riemannian manifold looks like on sufficiently small scales. | |
| Feb 24, 2016 at 19:54 | comment | added | Rbega | There are essentially two issues in these sorts of estimates: 1) Is there an $\epsilon$ sufficiently small so that if the total curvature is below this $\epsilon$ then the surface has pointwise bounded curvature and 2) Can one get an explicit bound on the pointwise curvature in terms of the total curvature. Point 1) is the more essential estimate and is a local statement and is most elegantly proved by blow up arguments as in the linked notes (note 8.12 holds in any Riemannian manifold). | |
| Feb 24, 2016 at 19:19 | comment | added | Andy Sanders | Dear Rbega, I found this note, but as it relies on previous estimates that don't seem "obviously true" outside of Euclidean space, I'm having a hard time following his proof. On another note, to make Choi-Schoen works, it seems one needs some favorable differential inequality derived from the Simon's Bochner formula for the second fundamental form, but there seems to be very little literature on this in general. In the end, I guess I'm going to have to get my hands dirty, but am I missing some silly? | |
| Feb 22, 2016 at 15:11 | history | edited | Rbega | CC BY-SA 3.0 |
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| Feb 22, 2016 at 14:52 | history | edited | Rbega | CC BY-SA 3.0 |
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| Feb 22, 2016 at 14:36 | history | answered | Rbega | CC BY-SA 3.0 |