Deformation of the Weighted Scalar Curvature
Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal ²ϕ-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particul...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212044 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Deformation of the Weighted Scalar Curvature. Pak Tung Ho and Jinwoo Shin. SIGMA 19 (2023), 087, 15 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862651008452132864 |
|---|---|
| author | Ho, Pak Tung Shin, Jinwoo |
| author_facet | Ho, Pak Tung Shin, Jinwoo |
| citation_txt | Deformation of the Weighted Scalar Curvature. Pak Tung Ho and Jinwoo Shin. SIGMA 19 (2023), 087, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal ²ϕ-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces.
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| first_indexed | 2026-03-15T15:33:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212044 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T15:33:05Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ho, Pak Tung Shin, Jinwoo 2026-01-23T10:11:32Z 2023 Deformation of the Weighted Scalar Curvature. Pak Tung Ho and Jinwoo Shin. SIGMA 19 (2023), 087, 15 pages 1815-0659 2020 Mathematics Subject Classification: 53C21; 53C23 arXiv:2311.02359 https://nasplib.isofts.kiev.ua/handle/123456789/212044 https://doi.org/10.3842/SIGMA.2023.087 Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal ²ϕ-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results. In particular, we define a weighted vacuum static space and study locally conformally flat weighted vacuum static spaces. We then prove some stability results of the weighted scalar curvature on flat spaces. Finally, we consider the prescribed weighted scalar curvature problem on closed smooth metric measure spaces. The authors would like to thank the referees for their comments and suggestions, which have improved the presentation of this paper. The first author was supported by the National Science and Technology Council (NSTC), Taiwan, with grant Number 112-2115-M-032-006-MY2, and the second author was supported by a KIAS Individual Grant (SP070701) via the Center for Mathematical Challenges at Korea Institute for Advanced Study. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Deformation of the Weighted Scalar Curvature Article published earlier |
| spellingShingle | Deformation of the Weighted Scalar Curvature Ho, Pak Tung Shin, Jinwoo |
| title | Deformation of the Weighted Scalar Curvature |
| title_full | Deformation of the Weighted Scalar Curvature |
| title_fullStr | Deformation of the Weighted Scalar Curvature |
| title_full_unstemmed | Deformation of the Weighted Scalar Curvature |
| title_short | Deformation of the Weighted Scalar Curvature |
| title_sort | deformation of the weighted scalar curvature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212044 |
| work_keys_str_mv | AT hopaktung deformationoftheweightedscalarcurvature AT shinjinwoo deformationoftheweightedscalarcurvature |