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PreprintarXiv licencearXiv

Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity

  • Mohammad Ghomi
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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 Mn with nullity index at least n−3. Consequently, the Euclidean isoperimetric inequality extends to Mn, which proves the Cartan-Hadamard conjecture for these spaces.

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Cite

BibTeXRIS
BibTeX
@misc{ghomi2026isoperimetric,
  title = {{Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity}},
  author = {Mohammad Ghomi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.24638},
  eprint = {2605.24638},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.24638},
}
RIS
TY  - UNPB
TI  - Isoperimetric and total curvature inequalities in Cartan-Hadamard manifolds with nullity
AU  - Mohammad Ghomi
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.24638
UR  - https://arxiv.org/abs/2605.24638
AB  - 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.
ER  -