Timeline for Estimating flat norm distance from a planar disc
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2010 at 22:25 | vote | accept | Sergei Ivanov | ||
| Mar 13, 2010 at 18:37 | answer | added | Anton Petrunin | timeline score: 4 | |
| Mar 13, 2010 at 5:20 | comment | added | Sergei Ivanov | No, the only proof I know is via compactness theorem. I know nothing about mean curvature flow but foresee problems. How to deal with the boundary and with topological singularities? | |
| Mar 12, 2010 at 18:32 | comment | added | Anton Petrunin | Did you try mean-curvature-flow? If yes (and if it works) what does it give you when $n$ grows? | |
| Mar 12, 2010 at 5:04 | comment | added | Sergei Ivanov | Yes a surface may be singular, it is just a map from a manifold. If n is large enough, you can approximate everything by immersions if you really need. On the constructive side, it is easier to work with singular chains rather than surfaces. | |
| Mar 12, 2010 at 0:38 | comment | added | Johannes Hahn | Okay, but there is still something wrong with this. If $S$ is not entirely above or below $D$ (more wave-like), then the gap between $S$ and $D$ is no manifold. | |
| Mar 11, 2010 at 22:58 | comment | added | Sergei Ivanov | No, $S-D$ is not $S\setminus D$. It is the formal sum of $S$ and $-D$ where $-D$ is $D$ taken with the opposite orientation. As a set, it equals $S\cup D$ for a generic surface. | |
| Mar 11, 2010 at 22:41 | comment | added | Johannes Hahn | Something's wrong with this "gap filling" stuff. Even in the easiest cases were $S$ is just a disc that has a small "dent" (say the surface {$(x,y,z) | x^2+y^2\leq 1, z=c\cdot(1-x^2+y^2)$}) the boundary of $F$ is $S\cup D$ not $S-D$. | |
| Mar 11, 2010 at 22:29 | history | asked | Sergei Ivanov | CC BY-SA 2.5 |