Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.07583 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908819427164160 |
|---|---|
| author | Chen, Jiaqi Fang, Yi Zhong, Jingyang |
| author_facet | Chen, Jiaqi Fang, Yi Zhong, Jingyang |
| contents | In this paper, we establish some comparison theorems for the total quotient curvature. Specifically, we examine the behavior of the functional with respect to the total quotient curvature and prove that the background Einstein metric achieves a sharp bound on the total quotient curvature. We prove that if the quotient curvature satisfies a point-wise lower (or upper) bound relative to the Einstein metric, then the corresponding integral inequality holds. Also we can show characterize the equality case. Our result generalizes the volume comparison theorem for scalar curvature and the rigidity results for $σ_k$-curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07583 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparison of total quotient curvature Chen, Jiaqi Fang, Yi Zhong, Jingyang Differential Geometry In this paper, we establish some comparison theorems for the total quotient curvature. Specifically, we examine the behavior of the functional with respect to the total quotient curvature and prove that the background Einstein metric achieves a sharp bound on the total quotient curvature. We prove that if the quotient curvature satisfies a point-wise lower (or upper) bound relative to the Einstein metric, then the corresponding integral inequality holds. Also we can show characterize the equality case. Our result generalizes the volume comparison theorem for scalar curvature and the rigidity results for $σ_k$-curvature. |
| title | Comparison of total quotient curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2602.07583 |