Unique continuation problem on RCD Spaces. I
In this note we establish the weak unique continuation theorem for caloric functions on compact <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 2) spaces and show that there exists an <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2024
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| Online Access: | https://hdl.handle.net/1721.1/153545 |
| _version_ | 1811096672514605056 |
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| author | Deng, Qin Zhao, Xinrui |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Deng, Qin Zhao, Xinrui |
| author_sort | Deng, Qin |
| collection | MIT |
| description | In this note we establish the weak unique continuation theorem for caloric functions on compact <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 2) spaces and show that there exists an <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 4) space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point . We also establish frequency estimates for eigenfunctions and caloric functions on the metric horn. In particular, this gives a strong unique continuation type result on the metric horn for harmonic functions with a high rate of decay at the horn tip, where it is known that the standard strong unique continuation property fails. |
| first_indexed | 2024-09-23T16:47:13Z |
| format | Article |
| id | mit-1721.1/153545 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:47:13Z |
| publishDate | 2024 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1535452024-09-20T18:42:29Z Unique continuation problem on RCD Spaces. I Deng, Qin Zhao, Xinrui Massachusetts Institute of Technology. Department of Mathematics Geometry and Topology In this note we establish the weak unique continuation theorem for caloric functions on compact <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 2) spaces and show that there exists an <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 4) space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point . We also establish frequency estimates for eigenfunctions and caloric functions on the metric horn. In particular, this gives a strong unique continuation type result on the metric horn for harmonic functions with a high rate of decay at the horn tip, where it is known that the standard strong unique continuation property fails. 2024-02-21T15:43:57Z 2024-02-21T15:43:57Z 2024-02-15 2024-02-18T04:12:27Z Article http://purl.org/eprint/type/JournalArticle 0046-5755 1572-9168 https://hdl.handle.net/1721.1/153545 Geometriae Dedicata. 2024 Feb 15;218(2):42 en 10.1007/s10711-024-00890-7 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Science and Business Media LLC Springer Netherlands |
| spellingShingle | Geometry and Topology Deng, Qin Zhao, Xinrui Unique continuation problem on RCD Spaces. I |
| title | Unique continuation problem on RCD Spaces. I |
| title_full | Unique continuation problem on RCD Spaces. I |
| title_fullStr | Unique continuation problem on RCD Spaces. I |
| title_full_unstemmed | Unique continuation problem on RCD Spaces. I |
| title_short | Unique continuation problem on RCD Spaces. I |
| title_sort | unique continuation problem on rcd spaces i |
| topic | Geometry and Topology |
| url | https://hdl.handle.net/1721.1/153545 |
| work_keys_str_mv | AT dengqin uniquecontinuationproblemonrcdspacesi AT zhaoxinrui uniquecontinuationproblemonrcdspacesi |