A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound
Year: 2026
Type: preprint
Abstract: We prove the generalized Cartan-Hadamard conjecture, also known as the Aubin conjecture, in the small volume regime under a lower Ricci curvature bound, for any dimension $n\geq 2$. More precisely, we show that if $(M^n,g)$ is a Cartan-Hadamard manifold satisfying $\mathrm{Sec}_g\leq\bar k\leq 0$ and $\mathrm{Ric}_g\geq (n-1)\underline k$, then its isoperimetric profile is at least that of the model space of curvature $\bar k$ for small enough volumes. We also reduce the proof of the generalized Cartan-Hadamard conjecture to establishing rigidity in the equality case.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213415861