Abstract: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.
| Comments: | 7 pages |
| Subjects: | Differential Geometry (math.DG) |
| MSC classes: | Primary 53C20, 53C21, Secondary 53C42, 52A40 |
| Cite as: | arXiv:2605.24638 [math.DG] |
| (or arXiv:2605.24638v1 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24638 arXiv-issued DOI via DataCite (pending registration) |
From: Mohammad Ghomi [view email]
[v1]
Sat, 23 May 2026 15:59:21 UTC (10 KB)
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