Nonconvex ancient solutions to curve shortening flow
We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t ≪ 0 it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α(t) = −t, and closed off by a small copy of the Grim Reaper translating soliton.
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Mathematical Society
2023
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| _version_ | 1826311818072555520 |
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| author | Zhang, Y Olson, C Khan, I Angenent, S |
| author_facet | Zhang, Y Olson, C Khan, I Angenent, S |
| author_sort | Zhang, Y |
| collection | OXFORD |
| description | We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t ≪ 0
it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α(t) = −t, and closed off by a small copy of the Grim Reaper translating soliton. |
| first_indexed | 2024-03-07T08:18:22Z |
| format | Journal article |
| id | oxford-uuid:37a2dde6-0c1c-4580-b7cc-a2e3f132c8fe |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:18:22Z |
| publishDate | 2023 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:37a2dde6-0c1c-4580-b7cc-a2e3f132c8fe2024-01-12T16:28:44ZNonconvex ancient solutions to curve shortening flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:37a2dde6-0c1c-4580-b7cc-a2e3f132c8feEnglishSymplectic ElementsAmerican Mathematical Society2023Zhang, YOlson, CKhan, IAngenent, SWe construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t ≪ 0 it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α(t) = −t, and closed off by a small copy of the Grim Reaper translating soliton. |
| spellingShingle | Zhang, Y Olson, C Khan, I Angenent, S Nonconvex ancient solutions to curve shortening flow |
| title | Nonconvex ancient solutions to curve shortening flow |
| title_full | Nonconvex ancient solutions to curve shortening flow |
| title_fullStr | Nonconvex ancient solutions to curve shortening flow |
| title_full_unstemmed | Nonconvex ancient solutions to curve shortening flow |
| title_short | Nonconvex ancient solutions to curve shortening flow |
| title_sort | nonconvex ancient solutions to curve shortening flow |
| work_keys_str_mv | AT zhangy nonconvexancientsolutionstocurveshorteningflow AT olsonc nonconvexancientsolutionstocurveshorteningflow AT khani nonconvexancientsolutionstocurveshorteningflow AT angenents nonconvexancientsolutionstocurveshorteningflow |