Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914596698193920 |
|---|---|
| author | Ghomi, Mohammad |
| author_facet | Ghomi, Mohammad |
| contents | Using the Chern-Gauss-Bonnet theorem, we establish a sharp inequality for the total Gauss-Kronecker curvature of convex hypersurfaces in Cartan-Hadamard manifolds $M^n$ with nullity index at least $n-3$. Consequently, the Euclidean isoperimetric inequality extends to $M^n$, which proves the Cartan-Hadamard conjecture for these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24638 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity Ghomi, Mohammad Differential Geometry Primary 53C20, 53C21, Secondary 53C42, 52A40 Using the Chern-Gauss-Bonnet theorem, we establish a sharp inequality for the total Gauss-Kronecker curvature of convex hypersurfaces in Cartan-Hadamard manifolds $M^n$ with nullity index at least $n-3$. Consequently, the Euclidean isoperimetric inequality extends to $M^n$, which proves the Cartan-Hadamard conjecture for these spaces. |
| title | Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity |
| topic | Differential Geometry Primary 53C20, 53C21, Secondary 53C42, 52A40 |
| url | https://arxiv.org/abs/2605.24638 |