Curvature-Dimension Condition Meets Gromov's n-Volumic Scalar Curvature

Jialong Deng Mathematisches Institut, Georg-August-Universität, Göttingen, Germany

Differential Geometry mathscidoc:2206.10004

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 17, (013), 2021.2
We study the properties of the n-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition CD(κ,n) was showed to imply Gromov's n-volumic scalar curvature ≥nκ under an additional n-dimensional condition and we show the stability of n-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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@inproceedings{jialong2021curvature-dimension,
  title={Curvature-Dimension Condition Meets Gromov's n-Volumic Scalar Curvature},
  author={Jialong Deng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220621161723488215419},
  booktitle={ Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)},
  volume={17},
  number={013},
  year={2021},
}
Jialong Deng. Curvature-Dimension Condition Meets Gromov's n-Volumic Scalar Curvature. 2021. Vol. 17. In Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220621161723488215419.
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