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PreprintarXiv licencearXiv

The generalized Cartan-Hadamard conjecture

  • Marcos Agnoletto
  • Márcio Fabiano Da Silva
  • Stefano Nardulli
  • Reinaldo Resende
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Abstract

We establish the generalized Cartan-Hadamard conjecture, including rigidity in the equality case. As a corollary, we obtain that isoperimetric regions are bounded. We prove the conjecture for Alexandrov spaces with two sided curvature bounds as well. A sharp Michael-Simon-type inequality for hypersurfaces in these spaces is also shown.

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Cite

BibTeXRIS
BibTeX
@misc{agnoletto2026generalized,
  title = {{The generalized Cartan-Hadamard conjecture}},
  author = {Marcos Agnoletto and Márcio Fabiano Da Silva and Stefano Nardulli and Reinaldo Resende},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37817},
  eprint = {2610.37817},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37817},
}
RIS
TY  - UNPB
TI  - The generalized Cartan-Hadamard conjecture
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.2610.37817
UR  - https://arxiv.org/abs/2610.37817
AB  - We establish the generalized Cartan-Hadamard conjecture, including rigidity in the equality case. As a corollary, we obtain that isoperimetric regions are bounded. We prove the conjecture for Alexandrov spaces with two sided curvature bounds as well. A sharp Michael-Simon-type inequality for hypersurfaces in these spaces is also shown.
ER  -