Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow
Abstract We study the stability and instability of ALE Ricci-flat metrics around which a Łojasiewicz inequality is satisfied for a variation of Perelman’s $$\lambda $$ λ...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2023
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| Online Access: | https://hdl.handle.net/1721.1/147090 |
| _version_ | 1826188353775599616 |
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| author | Deruelle, Alix Ozuch, Tristan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Deruelle, Alix Ozuch, Tristan |
| author_sort | Deruelle, Alix |
| collection | MIT |
| description | Abstract
We study the stability and instability of ALE Ricci-flat metrics around which a Łojasiewicz inequality is satisfied for a variation of Perelman’s
$$\lambda $$
λ
functional adapted to the ALE situation and denoted
$$\lambda _{{\text {ALE}}}$$
λ
ALE
. This functional was introduced by the authors in a recent work and it has been proven that it satisfies a good enough Łojasiewicz inequality at least in neighborhoods of integrable ALE Ricci-flat metrics in dimension larger than or equal to 5. |
| first_indexed | 2024-09-23T07:58:23Z |
| format | Article |
| id | mit-1721.1/147090 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T07:58:23Z |
| publishDate | 2023 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1470902024-02-05T06:21:08Z Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow Deruelle, Alix Ozuch, Tristan Massachusetts Institute of Technology. Department of Mathematics Abstract We study the stability and instability of ALE Ricci-flat metrics around which a Łojasiewicz inequality is satisfied for a variation of Perelman’s $$\lambda $$ λ functional adapted to the ALE situation and denoted $$\lambda _{{\text {ALE}}}$$ λ ALE . This functional was introduced by the authors in a recent work and it has been proven that it satisfies a good enough Łojasiewicz inequality at least in neighborhoods of integrable ALE Ricci-flat metrics in dimension larger than or equal to 5. 2023-01-13T13:01:24Z 2023-01-13T13:01:24Z 2023-01-12 2023-01-13T04:24:51Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/147090 Calculus of Variations and Partial Differential Equations. 2023 Jan 12;62(3):84 en https://doi.org/10.1007/s00526-022-02403-4 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. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Deruelle, Alix Ozuch, Tristan Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow |
| title | Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow |
| title_full | Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow |
| title_fullStr | Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow |
| title_full_unstemmed | Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow |
| title_short | Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow |
| title_sort | dynamical in stability of ricci flat ale metrics along the ricci flow |
| url | https://hdl.handle.net/1721.1/147090 |
| work_keys_str_mv | AT deruellealix dynamicalinstabilityofricciflatalemetricsalongthericciflow AT ozuchtristan dynamicalinstabilityofricciflatalemetricsalongthericciflow |