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Sponsored AI Networking Cookbook: Practical recipes for AI-assisted network automation and development AI Networking Cookbook: Practical recipes for AI-assisted network automation and development

Author

Shi-Bing Chen

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Preprint Sep 2026

The Cartan-Hadamard conjecture in dimension five

We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian $5$-manifolds of nonpositive sectional curvature, which establishes the Cartan-Hadamard conjecture in that dimension. The main step is a sharp inequality for constant-mean-curvature hypersurfaces, proved...

Shi-Bing Chen, M. Ghomi, Peng Wang · 3 citations · ⚡1
Preprint Sep 2026

The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds

We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian $n$-manifolds of nonpositive sectional curvature, $3\leq n\leq9$, which establishes the Cartan-Hadamard conjecture in these dimensions. The main step is a sharp inequality for constant-mean-curvature hype...

Shi-Bing Chen, M. Ghomi, Peng Wang · 1 citation

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