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PreprintCC BY 4.0arXiv

Sharp diameter estimates via integral geometry

  • Peter M. Topping
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Abstract

We prove that the diameter of a closed embedded surface in ℝ3 is always less than the integral of the magnitude of the mean curvature, divided by π. We also prove a sharp variant for surfaces with boundary, and apply it to address a conjecture of Miura.

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Cite

BibTeXRIS
BibTeX
@misc{topping2026sharp,
  title = {{Sharp diameter estimates via integral geometry}},
  author = {Peter M. Topping},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34367},
  eprint = {2610.34367},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34367},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sharp diameter estimates via integral geometry
AU  - Peter M. Topping
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34367
UR  - https://arxiv.org/abs/2610.34367
AB  - We prove that the diameter of a closed embedded surface in ℝ^3 is always less than the integral of the magnitude of the mean curvature, divided by π. We also prove a sharp variant for surfaces with boundary, and apply it to address a conjecture of Miura.
ER  -