Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature
We study the properties of the n-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition CD(κ, ) was shown to imply Gromov's -volumic scalar curvature ≥ κ under an additional -dimensional condition, and we show the stability of -volumic scalar curvature ≥...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211175 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature. Jialong Deng. SIGMA 17 (2021), 013, 20 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732250500562944 |
|---|---|
| author | Deng, Jialong |
| author_facet | Deng, Jialong |
| citation_txt | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature. Jialong Deng. SIGMA 17 (2021), 013, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the properties of the n-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition CD(κ, ) was shown to imply Gromov's -volumic scalar curvature ≥ κ under an additional -dimensional condition, and we show the stability of -volumic scalar curvature ≥ κ with respect to smGH-convergence. Then we propose a new weighted scalar curvature on the weighted Riemannian manifold and show its properties.
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| first_indexed | 2026-04-17T15:31:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211175 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:31:45Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Deng, Jialong 2025-12-25T13:22:30Z 2021 Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature. Jialong Deng. SIGMA 17 (2021), 013, 20 pages 1815-0659 2020 Mathematics Subject Classification: 53C23 arXiv:2001.04087 https://nasplib.isofts.kiev.ua/handle/123456789/211175 https://doi.org/10.3842/SIGMA.2021.013 We study the properties of the n-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition CD(κ, ) was shown to imply Gromov's -volumic scalar curvature ≥ κ under an additional -dimensional condition, and we show the stability of -volumic scalar curvature ≥ κ with respect to smGH-convergence. Then we propose a new weighted scalar curvature on the weighted Riemannian manifold and show its properties. I am grateful to Thomas Schick for his help, the referees for their useful comments, and the funding from the China Scholarship Council. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature Article published earlier |
| spellingShingle | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature Deng, Jialong |
| title | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature |
| title_full | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature |
| title_fullStr | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature |
| title_full_unstemmed | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature |
| title_short | Curvature-Dimension Condition Meets Gromov's -Volumic Scalar Curvature |
| title_sort | curvature-dimension condition meets gromov's -volumic scalar curvature |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211175 |
| work_keys_str_mv | AT dengjialong curvaturedimensionconditionmeetsgromovsvolumicscalarcurvature |