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Blaschke--Santal{ó} diagram for the volume, the diameter, and the Cheeger constant

  • Zakaria Fattah
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Abstract

We study the Blaschke--Santal{ó} diagram associated with the volume, the diameter, and the Cheeger constant. In the class of bounded open subsets of ℝm, m≥ 2, we give a complete description of the diagram. In the class of convex bodies of ℝm, we prove that the diagram is closed and simply connected as it is given by the region between two continuous functions for which qualitative properties such as monotonicity, local behavior, and growth estimates are studied.

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Cite

BibTeXRIS
BibTeX
@misc{fattah2026blaschkesantaló,
  title = {{Blaschke--Santaló diagram for the volume, the diameter, and the Cheeger constant}},
  author = {Zakaria Fattah},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00337},
  eprint = {2609.00337},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00337},
}
RIS
TY  - UNPB
TI  - Blaschke--Santal{ó} diagram for the volume, the diameter, and the Cheeger constant
AU  - Zakaria Fattah
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00337
UR  - https://arxiv.org/abs/2609.00337
AB  - We study the Blaschke--Santal{ó} diagram associated with the volume, the diameter, and the Cheeger constant. In the class of bounded open subsets of ℝ^m, m≥ 2, we give a complete description of the diagram. In the class of convex bodies of ℝ^m, we prove that the diagram is closed and simply connected as it is given by the region between two continuous functions for which qualitative properties such as monotonicity, local behavior, and growth estimates are studied.
ER  -