| dc.contributor |
Massachusetts Institute of Technology. Department of Mathematics |
|
| dc.creator |
Lam, Casey |
|
| dc.creator |
Lauer, Joseph |
|
| dc.date |
2021-12-17T17:10:27Z |
|
| dc.date |
2021-09-20T17:30:56Z |
|
| dc.date |
2021-12-17T17:10:27Z |
|
| dc.date |
2018-12 |
|
| dc.date |
2020-09-24T21:45:37Z |
|
| dc.date.accessioned |
2023-03-01T18:09:43Z |
|
| dc.date.available |
2023-03-01T18:09:43Z |
|
| dc.identifier |
https://hdl.handle.net/1721.1/131919.2 |
|
| dc.identifier.uri |
http://localhost:8080/xmlui/handle/CUHPOERS/278983 |
|
| dc.description |
In this note we prove that the level-set flow of the topologist’s sine curve is a smooth closed curve. In Lauer (Geom Funct Anal 23(6): 1934–1961, 2013) it was shown by the second author that under the level-set flow, a locally connected set in the plane evolves to be smooth, either as a curve or as a positive area region bounded by smooth curves. Here we give the first example of a domain whose boundary is not locally connected for which the level-set flow is instantaneously smooth. Our methods also produce an example of a nonpath-connected set that instantly evolves into a smooth closed curve. |
|
| dc.format |
application/octet-stream |
|
| dc.language |
en |
|
| dc.publisher |
Springer US |
|
| dc.relation |
https://doi.org/10.1007/s12220-017-9868-2 |
|
| dc.rights |
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. |
|
| dc.rights |
Mathematica Josephina, Inc. |
|
| dc.source |
Springer US |
|
| dc.title |
The level-set flow of the topologist’s sine curve is smooth |
|
| dc.type |
Article |
|
| dc.type |
http://purl.org/eprint/type/JournalArticle |
|