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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2021
Автор: Deng, Jialong
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2021
Онлайн доступ: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
Цитувати: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
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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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last_indexed 2026-04-17T15:31:45Z
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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