Timeline for Solution of Plateau Problem for a simple, smooth closed curve on a Riemannian Manifold (Kahler) gives a surface that can be parametrized by a closed disk?
Current License: CC BY-SA 2.5
4 events
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| Jan 24, 2011 at 22:08 | comment | added | Dan Lee | Not an expert, but I'll add one bit to (part 4 of) this excellent answer: Given a boundary, you can always find an area-minimizing rectifiable current with the given boundary. Almgren's big regularity paper says that the interior of this minimizer is an embedded smooth manifold away from a Hausdorff codimension two singular set. In the case where the boundary is 1-dimensional, Sheldon Chang further showed that the singular points are isolated classical branch points. | |
| Jan 17, 2011 at 13:06 | vote | accept | Italo | ||
| Jan 16, 2011 at 0:45 | comment | added | Italo | Thank you very much for the detailed answer! I'll wait a little more before accepting it because i want to see if you or someone has anything else to say. | |
| Jan 15, 2011 at 15:30 | history | answered | Bill Thurston | CC BY-SA 2.5 |