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PreprintarXiv licencearXiv

A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound

  • Marcos Agnoletto
  • Márcio Fabiano Da Silva
  • Stefano Nardulli
  • Reinaldo Resende
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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≥ 2. More precisely, we show that if (Mn,g) is a Cartan-Hadamard manifold satisfying Secg≤k̅≤ 0 and Ricg≥ (n−1)underline k, then its isoperimetric profile is at least that of the model space of curvature k̅ for small enough volumes. We also reduce the proof of the generalized Cartan-Hadamard conjecture to establishing rigidity in the equality case.

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Cite

BibTeXRIS
BibTeX
@misc{agnoletto2026proof,
  title = {{A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound}},
  author = {Marcos Agnoletto and Márcio Fabiano Da Silva and Stefano Nardulli and Reinaldo Resende},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.17093},
  eprint = {2609.17093},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17093},
}
RIS
TY  - UNPB
TI  - A proof of the Cartan-Hadamard conjecture for small volumes under a Ricci curvature lower bound
AU  - Marcos Agnoletto
AU  - Márcio Fabiano Da Silva
AU  - Stefano Nardulli
AU  - Reinaldo Resende
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2609.17093
UR  - https://arxiv.org/abs/2609.17093
AB  - 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≥ 2. More precisely, we show that if (M^n,g) is a Cartan-Hadamard manifold satisfying Sec_g≤k̅≤ 0 and Ric_g≥ (n−1)underline k, then its isoperimetric profile is at least that of the model space of curvature k̅ for small enough volumes. We also reduce the proof of the generalized Cartan-Hadamard conjecture to establishing rigidity in the equality case.
ER  -